To the mods and everyone else: it seems to me that this question leans strongly toward linguistics and so might be answered by someone who -- like me -- is not a historian. Perhaps you'll agree?

To OP: first of all, I would look at the assumptions behind your question.

There is certainly variation in the renderings of "Muhammad" in non-Arabic languages. For example, we see "Mehmet" in Turkey, "Mamadou" in various parts of west Africa, "Mokhmad" in parts of the Caucasus region, etc.

And, on the other hand, when English speakers see names for Jesus that vary greatly from the usual English name, we need to understand that it is English that is the odd one out. Jesus is called something like yay-soos or ee-soo in most of the non-English-speaking world, not jee-zus as in English. English took its spelling for the name "Jesus" from continental European sources, but the pronunciation was changed due, in part, to what linguists call "The Great Vowel Shift", which altered the pronunciation of vowels in English from the Latin-based pronunciation standard that is largely followed in most languages written using the Roman alphabet.

Still, there is something to what you say. I would argue that there are two main reasons for what you observe.

First, Christianity and Islam have had very different attitudes toward languages.

Early Christians began their collection of sacred writings with the Tanakh, a collection of writings gathered over centuries by the Jewish people, and written mostly in Ancient Hebrew with a smattering of Aramaic. However, living in the aftermath of the conquests of Alexander the Great, Christians initially preferred Greek. Then, with the strong influence of the church of Rome somewhat early on in Christianity, Latin began to be used extensively. As a result of all this, Christianity and the Christian Bible have been multilingual from the start.

This presented issues early on in the rendering of names. In his own culture, Jesus would have been called something like Yeshua. But when early Christians began to spread their message in Greek-speaking cultures, they had to deal with the fact that Greek had no "sh" sound, and it required endings on all nouns, including names. Thus, Jesus became known as "Ιησούς" in Greek, which is pronounced essentially the same as the yay-soos that much of the world still knows him as today.

In contrast, Islam has always been centered on Arabic, and has placed great value on that language. The Qu'ran was not gathered over centuries from multiple writers in varying cultures. It is written in a single language and seems to have been put together by one man over a period of less than 25 years (the early history of Islam is sometimes a bit murky). As Muslims spread their message, they spread the Arabic language with it.

One result is that the Arabic text of the Qu'ran is the only thing that gets called "Qu'ran". Christians might refer to the English translations of their sacred writings as "the Bible", but Muslims have always made a clear distinction between the Qu'ran itself and translations of the Qu'ran into other languages. And the handling of names has been influenced by these very different traditions.

Second, in recent decades in western culture there have been calls for greater respect to be paid to non-western cultures. And part of this involves pronouncing non-western proper names in ways that are closer to the pronunciation in the original languages. Thus, in English, "Peking" has been replaced by "Beijing", and so on. Thus, out of respect for traditional Arab/Muslim culture, we have largely standardized on "Muhammad", with earlier spelling/pronunciation variants being frowned upon.

On the other hand, while Jesus came from the Middle East, Christianity is generally seen, in the west, as a western thing. It is thus not regarded as something western culture has oppressed, which needs to be granted greater respect; it is seen as a tool of Western oppression.

There is actually a movement that says Jesus should be called "Yeshua" (or "Y'shua"). It seems to be most prominent among people identifying as Jewish Christians. However, this movement has not been hugely influential, and it has received very little attention from the mainstream press.