Why did the coins of England minted under Richard I and John bear the name of Henry?

I don't know why Richard or John wouldn't get around to changing the name on the coins, especially if they did change the dates on the coins. And if they didn't change the dates on the coins, how do coin experts know there are coins from the reigns of Richard and John with the name of Henry?

One sort of analogous situation is the continued minting of Maria Theresa silver thalers for use in trade in the Middle East.

Maria Theresa was Archduchess of Austria, Queen of Hungary and Croatia, etc., Queen of Bohemia, duchess and countess of various places, etc., etc., from 1740 to 1780, and wife of Emperor Francis I from 1745-1765.

The 1780 Maria Theresa thalers became so popular for trade that other countries started minting them.

The MTT quickly became a standard trade coin and several nations began striking Maria Theresa thalers. The following mints have struck MTTs: Birmingham, Bombay, Brussels, London, Paris, Rome and Utrecht, in addition to the Habsburg mints in Günzburg, Hall, Karlsburg, Kremnica, Milan, Prague, and Vienna. Between 1751 and 2000, some 389 million were minted. These various mints distinguished their issues by slight differences in the design, with some of these evolving over time.[4] In 1935 Mussolini gained a 25-year concession over production of the MTT. The Italians blocked non-Italian banks and bullion traders from obtaining the coin and so France, Belgium, and the UK started producing the coin so as to support their economic interests in the Red Sea, Persian Gulf and East Coast of Africa. In 1961 the 25-year concession ended and Austria made diplomatic approaches to the relevant governments requesting they cease production of the coin. The UK was the last government to formally agree to the request in February 1962.

The MTT came to be used as currency in large parts of Africa and Middle East until after World War II. It was common from North Africa to Somalia, Ethiopia, Kenya, and down the coast of Tanzania to Mozambique. Its popularity in the Red Sea region was such that merchants would not accept any other type of currency. The Italian government produced a similar designed coin in the hope of replacing the Maria Theresa thaler, but it never gained acceptance.[5]

The Maria Theresa thaler was also formerly the currency of the Hejaz, Yemen, the Aden Protectorate as well as Muscat and Oman on the Arabia peninsula. The coin remains popular in North Africa and the Middle East to this day in its original form: a silver coin with a portrait of the buxom empress on the front and the Habsburg Double Eagle on the back.[6]

I believe that the Austrian Mint occasionally produced new Maria Theresa thalers as recently as the late 20th century or even in the 21st century.

So that is a much more extreme example of using the name of a deceased ruler on coins for a much longer time.

I don't know, but it might be possible that there would be a similar motive for keeping the name of Henry II on coins produced after his death.

Robert Bartlett, professor of Medieval History at the University of St Andrews, has written that the success of Henry II's short cross type coinage issued in 1180

was so great that no one was willing even to tamper with its inscription, so that English pennies bore the legend 'King Henry' throughout the reigns of Richard I and John.

Source: Robert Bartlett, 'England under the Norman and Angevin Kings: 1075-1225' (OUP, 2002)

Lucia Travaini, numismatist at the University of Milan, cites several examples in medieval Europe of largely unchanged coinage despite a change in rulers (and even in dynasties), writing that

the primary reason for not altering the iconography was to make such coins easily identifiable for their good and reliable quality (although this did tend to diminish over time).

Source: Lucia Travaini, 'Coins, Images, Identity, and Interpretations'. In S. Solway (ed) 'Medieval Coins and Seals' (2015)

Travaini includies the short cross coins of the reigns of Richard I and John among her examples (mentioned in a footnote). Thus, the coins may be seen to express the continuity of the Angevin empire which Henry II founded and built.

It was, in fact, not uncommon for French rulers to 'immobilize' their coinage:

While this may seem strange to us, and was a departure from the practice of earlier English kings, there was a precedent for such “immobilisation” of coins on the Continent.

England at this time was ruled by Richard as part of the vast Angevin domain his father had inherited and expanded which covered not only England but parts of Ireland and most of western France. In much of feudal France immobilised coins were common place and in particular in the Angevin heart-lands

Source: Richard Kelleher, 'Kings and Coins in Medieval England'

However, the short cross coins were only partially immobilised during the time they were issued, from 1180 to 1247. Numismatists have identified 8 classes spanning the reigns of four kings thus:

• Henry II [1154-1189]: Class 1
• Richard I [1189-1199]: Classes 2-4
• John [1199-1216]: Classes 4-6
• Henry III [1216-1272]: Classes 6-8

The above cited article, The Short Cross coinage (1180 - 1247 AD) details differences between the classes of coins, but notes that all the coins had he following "general appearance"

Obverse: From 10 o'clock the legend hENRICVS REX around a crowned and bearded bust. In the king's right hand is a sceptre which divides the R from the EX .

Reverse: +(Name of moneyer) ON (mint name) around a small voided cross with quatrefoils in the angles.

John's reign included the re-coinage of 1205 mentioned by the OP. By this time, the Angevin empire that his father had built had mostly been lost, and his reputation fell far short of that of his predecessors. This could be an additional reason why he continued to use his father's name on the coins (in addition to the aforementioned reasons, success and easily identifiable). One could also venture that the message was that Henry II's Angevin empire was still going strong. This was far from reality, of course, but reality didn't stop English monarchs claiming to be kings of France long after Henry V's conquests were lost. In short, the drawbacks of continuing with the same basic design (mentioned by sempaiscuba in a comment below) were outweighed by the advantages.

Also in a comment below, sempaiscuba has pointed out that both Richard and John issued coins in their own name in Aquitaine / Poitou and Ireland respectively.

Why did they do this, yet retain Henry II on the short cross coins? I haven't found an academic source explaining this, so can only offer my opinion on this:

Richard (Aquitaine and Poitou) and John, (Ireland) were granted these territories before they became kings, and started issuing coins there in their own names, also before they became kings. Coins can be a way of establishing authority (i.e. propaganda). The brothers were also in dispute at various times with their father, so issuing coins in their own names could also be seen as emphasizing their independence.

That they continued to issue coins in their own names in these regions after they became kings was probably due to the simple fact such coins were already in circulation, so why change?