These are very confusing, even for Latin ones and all are still full of uncertainties and speculation, apparently stemming from quite some influence asserted cross-culturally and confusion among the ancients which star/planet to name exactly how. What follows is quite likely, but not definitive.

For it seems clear is that there are indeed pre-Islamic and genuinely Arabic origins for the names. But the connection to gods and goddesses seems backward. We do not see a god first and then a star named after that god. Instead we see words for concepts and meanings that are attributes for a star and a god. And all astronomy is really heavily influenced by Mesopotamian and especially Babylonian astronomy and its traditions. Which then spreads to the West and to the East, or strictly speaking South, for Arabian language names…

This is even evidenced in Hebrew, were sedeq generally means righteousness and justice, attributes of God, as well simply Jupiter.

For Jupiter, in Arabic المشتري al Mustari, things are quite strange:

If you machine translate the Arabic Wikipedia page, it currently alternates in the text with the Western name Jupiter and the Arabic meaning of the word: buyer/purchaser/client.

That might invite a lot of folk etymology.

In 1935, experts were still wholly unsure how to explain this bizarre-sounding tradition:

I am not aware of an explanation for al-Mustari, the Arabic name for the planet Juppiter. Nor is there any reference to one in the recently published article in the Encyclopaedia of Islam. The name can hardly have anything to do with the usual appellative meaning of al-mustari "buyer, customer".

— H Bauer: "Al-Mustari", Orientalistische Literaturzeitung, Volume 38 Issue 1-6, 1935, p477, doi

The article goes on to speculate that in old Semitic languages the three brightest objects in the night sky — Moon, Venus, Jupiter — were origanlly named after exactly that: their brightness, making the Jupiter just: the Radiant One.

This is speculation. In Hebrew for example the real etymology for Moon is not entirely certain and may simple hark back to "the wanderer".

Complementing the theory for Jupiter as the Radiant one is for example another etymology that traces Jupiter's name back in time to connect via weighing evidence for and against it to Akkadian language and a word for Mercury at the same time:

Mustarilu may be a West-Semitic name compositum, but it is not a true Akkadian word. The Babylonian and Akkadian spellings are ambiguous, a direct connection to Hebrew, Phoenician or Aramaic seems implausible. The fist plausible reconstruction might be akin to "Detaching-God", when used for Mercury, which is always near the sun.

If Mustarilu is an Old-Arabic word, while it appears to have been a loan word in any case, then it may have been used at first more like "a certain star", and thus for Mercury as well.

Accordingly, al-mustari was understood as "the shining one", seeing in the name the participle of istara "to shine". It still needs to be verified whether this istara was really used in addition to istara "to buy" in the oldest language.

— Wolfram von Soden: "Akkadisch muštarîlu „Merkur“ und arabisch muštarï, türkisch müşterï, „Jupiter“", Wiener Zeitschrift für die Kunde des Morgenlandes , 1969, Vol. 62, Festschrift HERBERT JANSKY Zum 70. Geburtstag gewidmet von seinen Freunden und Schülern (1969), pp.83–86

More systematically, from a very comprehensive analysis across most Old World cultures delivered by Eilers, Arabic planet names for Mercury, Venus, Mars, Jupiter, Saturn are:

'Utärid, az-Zuhara, Mirrïh, al-Mustarï, Zuhal
[…]

Noting again the correspondence in Greek for Mercury: using either the Babylonian Sahitu as Σεχες or Στιλβων for "the radiant one", officially Ερμής/hermes/Mercury. However, the most common Arabic name for Mercury is Utarid, meaning "the fast moving one", from the Semitic root tarada (the parallelism for Mercury/Hermes the messenger of the gods seems obvious).

Venus, named Zuh(a)ra or al-'Uzza or 'Aziz, has for Zuhara the root z h r and thus again "shining, radiate", similar to al-azharan, the two shining ones, that is sun and moon.

Mars in Arabic is Mirrïh, with an unknown etymology. The options are: The direct root maraha would be anoint or rub, clearly not a good choice. Aramaic roots for a loanword might be mrh (cheerful, happy), the roughly same letters in Syriac would mean "to appear boldly, to be difficult", going into rebellious, troublemaker etc. Another option might be Iranian/Persian import: Mirrih < *marrih < *marniχ < *marnika- — "the deadly one"; but an Iranian loanword would be quite exceptional here. Yet another option favoured by Eilers might be marh as found in a word for a tree used as tinder (marih/mirrih then now meaning weak/soft), thus giving a genuine Arabic connection for fire-bringer.

For Jupiter, Eilers also settles on "the radiant one", based on a range of Arabian radicals but connects it as well to Akkadian mesrum (plentifulness) — directly rejecting Soden's mustarilu suggestion (claiming only mustatallu to be the correct reading)!

Saturn has two names in Arabic lands, Kaiwan (the slow one, going back to Akkadian and Babylonian forms) and Zuhal. Zuhal has again multiple candidates for an explanation: 1. from the radical zhl, 'to move away', since Saturn moves about in the 7th sphere of the sky. 2. Zuhalun would mean, Saturn does not lead the other planets but lags far behind them.

Summary for Eilers and his theories:

— Wilhelm Eilers: "Sinn und Herkunft der Planetennamen", Verlag der Bayerischen Akademie der Wissenschaften: München, 1976. (gBooks, PDF)

For a less flowery and 'direct to earth' corroboration, mostly in line with Eilers:

Mercury

عُطَارِد • (ʿuṭārid) m

(astronomy) Mercury (planet)

Etymology Ultimately unknown, without known Semitic cognates:

Natively coined from the root ط ر د‎ (ṭ-r-d) meaning, "to chase or chase away", "to race or race after", "to cause something to pick up speed", "to outstrip", "follow swiftly"; related to the planet having the shortest orbital period and its eccentric periods of velocity, an association found cross-culturally via observation. The atypical /ع/ occurs occasionally in some Arabic dialects in replacement of /أ/ due to the pharyngeal-aspect of a nearby emphatic consonant, namely /ط/. A variation of ع ط د‎ (ʿ-ṭ-d) meaning "to be extreme" in many senses including "to go at a very quick pace", "to be most hasty", "a very quick rate of going". Alternatively, potentially a synthesis of both roots, as such blends are a known source of etymology for some quadriliteral roots.

Venus

الزهرة

Arabic Etymology Related to زُهْرَة‎ (zuhra, “brilliance, brightness, radiance, beauty”); Venus is the brightest object in the night sky (except the moon).

Proper noun الزُّهَرَة • (az-zuhara) f (astronomy) Venus (planet)

Mars

Etymology From the root م ر خ‎ (m-r-ḵ), meaning "to rub", "to leak sap (especially flammable oils)", "to anoint or cover in oil", "to rub together flammable branches"; stemming from the red color of the planet being associated with fire, a conception found in archaic synonyms as well.

Proper noun اَلْمِرِّيخ • (al-mirrīḵ) m

(astronomy) the planet Mars ‏ اَلْمِرِّيخُ هُوَ ٱلْكَوْكَبُ ٱلرَّابِعُ فِي ٱلْبُعْدِ عَنِ ٱلشَّمْسِ فِي ٱلنِّظَامِ ٱلشَّمْسِيِّ وَهُوَ ٱلْجَارُ ٱلْخَارِجِيُّ لِلْأَرْضِ وَيُصَنَّفُ كَوْكَبًا صَخْرِيًّا، مِنْ مَجْمُوعَةِ ٱلْكَوَاكِبِ ٱلْأَرْضِيَّةِ.‎‎ al-mirrīḵu huwa l-kawkabu r-rābiʿu fī l-buʿdi ʿani š-šamsi fī n-niẓāmi š-šamsiyyi wahuwa l-jāru l-ḵārijiyyu lilʾarḍi wayuṣannafu kawkaban ṣaḵriyyan, min majmūʿati l-kawākibi l-ʾarḍiyyati. Mars is the fourth planet in distance from the Sun in the Solar System and it is Earth's external neighbor and is classified as a rocky planet from the group of the Terrestrial Planets.

Jupiter

Etymology
From مُشْتَرٍ‎ (muštarin, “buyer, seller”), from the root ش ر ي‎ (š-r-y) with the original semantic sense of bringing of goods or commodities (to be exchanged). This renders the title to mean "the bringer of goods", "provider of commodities", or "supplier of fortunes"; parallel with the planet's other names also denoting fortune and its auspicious nature.

Alternatively from the root ش ر ي‎ (š-r-y) in the sense of "being persistent", "to be reliable"; possibly parallel with the title صَدِيق‎ (ṣadīq) and Hebrew צֶדֶק‬‎ (tzédek), which however can also be interpreted as "charitable", "giving", or "honoring". Possible distant relation to Akkadian 𒀭𒈪𒁲𒊑 (mīšāru, “uprightness; god personifying justice”) and Ugaritic 𐎎𐎌𐎗 (mšr, “righteousness”), cognate with Hebrew יָשָׁר‎ (yashár, “upright, right, correct”) and يَسْر‎ (yasr). The root ي س ر‎ (y-s-r) also however denotes "to procure goods easily", "to be or grow rich", "to live in affluence or ease", "to have good fortune".

Proper noun

الْمُشْتَرِي • (al-muštarī) m

(astronomy) Jupiter (planet)

Saturn

Etymology
From the root ز ح ل‎ (z-ḥ-l) meaning "to be distant or remote", "to linger away from others"; so called as it is the furthest and has the slowest orbital period of the classical seven heavenly bodies (counting the Sun and the Moon, without the inclusion of Earth).

Proper noun زُحَل • (zuḥal) m

Saturn (planet) Declension زُحَل (zuḥal)

Synonyms كَيْوَان‎ (kaywān, “one that stays, one that lingers”) نَكْرُه‎ (nakruh), نِكْرَة‎ (nikra, “one who seems unfamiliar, one who is foreign or estranged, distant or alien”) النَحْسَانِ‎ (an-naḥsāni, “the two misfortunes”), paired with Mars, contrasted with Venus and Mercury, or Venus and Jupiter in another tradition النَحْس الأَكْبَر‎ (an-naḥs al-ʾakbar, “the greater misfortune”), contrasted with Mars the lesser

Descendants Persian: زحل‎ (Zohal) → Middle Armenian: Զօհալ (Zōhal), Զոհալ (Zohal)

For funny results:

Concerning direct pre-Islamic Arabian religion and some possible connections of stars in the sense of planets to those gods prevalent in the region:

Al-Uzza is not only an alternative name for Venus as listed above. She was one of the three chief goddesses of the old-Arabian religion and especially the Quraysh

Uzza Name given to the star Venus by the Banu Ghatafan of Arabia, who worshipped her in the form of an acaciatree. One of the three gods whom Mahomet would not recognize, the others being Allat and Manat.

— Edgerton Skyes & Alan Kendall: "Who's Who in Non-Classical Mythology", Routledge: London, 1993. p201.)

To drive home that not too much meaning should be interpreted as 'definitive' into these names: Note that this makes for an interesting complication since Venus, Ishtar, Astarte and Asherah can at various points all represent the same thing, of course differently, and then these ladies then were often associated with Baal, Bel, El (including when syncretized into Jahwe), Jupiter as the highest being or chief of the club. On the other hand in Ugarit Venus was called Salem (Shalim), the Evening Star. A name which appears to be preserved in ‘Jerusalem’. And now He was the son of El.

Another connection to ancient Arabian gods is again found between Gad and Jupiter, although not in the currently most popular Arabic name for Jupiter, but in the wider associations:

Gad was the name of the pan-Semitic god of fortune, usually depicted as a male but sometimes as a female and is attested in ancient records of Aram and Arabia. Gad is also mentioned in the bible as a deity in the Book of Isaiah (Isaiah 65:11 – some translations simply call him (the god of) Fortune), as having been worshipped by a number of Hebrews during the Babylonian captivity. Gad apparently differed from the god of destiny, who was known as Meni. The root verb in Gad means cut or divide, and from this comes the idea of fate being meted out.

It is possible that the son of Jacob named Gad is named after Gad, or that Gad is a theophoric name, or a descriptive. Although the text presents a different reason, the (ketub) quotation of Zilpa (Gad's mother) giving the reason of Gad's name could be understood that way.

How widespread the cult of Gad, the deity, was in Canaanite times may be inferred from the names Baalgad, a city at the foot of Mount Hermon, and Migdal-gad, in the territory of Judah. Compare also the proper names Gaddi and Gaddiel in the tribes of Manasseh and Zebulun (Numbers 13:10, 11). At the same time it must not be supposed that Gad was always regarded as an independent deity. The name was doubtless originally an appellative, meaning the power that allots. Hence any of the greater gods supposed to favour men might be thought of as the giver of good fortune and be worshiped under that title; it is possible that Jupiter, the planet, may have been the Gad thus honoured - among the Arabs the planet Jupiter was called the greater Fortune (Venus was styled the lesser Fortune).

In general, pre-Islamic Arabian religion was quite fragmented in their detailed pantheons. Most tribes having their own set of specialists with comparable but different attributes and names. However, those they do have really in common are mostly those associated with the trinity of Sun, Moon and Venus. Those may differ quite a bit in naming then, and Uzza seems to be basically the only form of such a name surviving to this day as a major known alternative name. Critically speaking, Venus is also the only actual planet for which knowledge among the earlier pre-Islamic Central Arabs is firmly attested.

Of the planets, only Venus (Arabic Zuhara, Zuhra) can be shown with certainty to be known, probably Mercury as well.
[…]
The investigation has shown that some conventional ideas of the star cult in Arabia have to be considerably reduced. While in the ancient South Arabian civilisations as well as in ancient Mesopotamia religion had a strong astral character, Central and Northern Arabia possessed a certain (and not too insignificant) degree of practical knowledge of the stars, as well as a stock of star myths and ideas about the effects of the stars, which have certainly only been preserved in scattered fragments; an actual cult, however, can only be claimed for the star of Venus, and even here only with a high degree of probability.

— Joseph Henninger: "Arabica sacra: Contributions à l’histoire religieuse de l’Arabie et de ses régions limitrophes/ Aufsätze zur Religionsgeschichte Arabiens und seiner Randgebiete", ch.: "Über Sternkunde und Sternkult In Nord- und Zentralarabien" (1954), Vandenhoeck & Ruprecht: Göttingen, 1981. (doi online version)