Upvote:1
Josephus needs to be read with certain items in mind.
He likely had a complicated relationship involving the Imperial Court, and any subject related to past Judean insurrection. A reasonable position might assume, Josephus was intending for accurate details to be recorded for posterity, but he may have primarily been focused on an audience of one as he recollected. The Ceasar.
The narrative contained in Acts would be substantially different.
Upvote:2
According to scholars Jamieson, Fausset, & Brown, they say the Thaedus was different from the one mentioned in Josephus.
35-39. Theudas--not the same with a deceiver of that name whom JOSEPHUS mentions as heading an insurrection some twelve years after this [Antiquities, 20.5.1], but some other of whom he makes no mention. Such insurrections were frequent.
37. Judas of Galilee--(See on JF & B for Lu 2:2, and Luk 13:1-3 ) [JOSEPHUS, Antiquities, 13.1.1].
Matthew Henry asserts the same; that the two were different and provides some explanation.
(2.) The case was the same with Judas of Galilee, v. 37. Observe, [1.] The attempt he made. It is said to be after this, which some read, besides this, or, Let me mention, after this,-supposing that Judas's insurrection was long before that of Theudas; for it was in the time of the taxation, namely, that at our Saviour's birth (Lu. 2:1), and that of Theudas, whom Josephus speaks of, that mutinied, in the time of Cuspius Fadus; but this was in the days of Claudius Caesar, some years after Gamaliel spoke this, and therefore could not be the same. MH
Thayer's Greek Lexicon has this to say.
Θευδᾶς [probably contracted from θεόδωρος, Winers Grammar, 103 (97); especially Bp. Lightfoot on Colossians 4:15; on its inflection cf. Buttmann, 20 (18)], ὁ, Theudas, an impostor who instigated a rebellion which came to a wretched end in the time of Augustus: Acts 5:36. Josephus (Antiquities, 20, 5, 1) makes mention of one Theudas, a magician, who came into notice by pretending that he was a prophet and was destroyed when Cuspius Fadus governed Judæa in the time of Claudius. Accordingly, many interpreters hold that there were two insurgents by the name of Theudas; while others, with far greater probability, suppose that the mention of Theudas is ascribed to Gamaliel by an anachronism on the part of Luke. On the different opinions of others cf. Meyer on Acts, the passage cited; Winers RWB, under the word; Keim in Schenkel see 510f; [especially Hackett in B. D., under the word]. TGL
See here for more details.
To answer the OP, no Gamaliel did not get the names and chronologies wrong.