Should “Jesus” be rendered “Yeshu‘a” in English?

I would say it does not necessarily matter unless you choose to believe so, because belief has important bearing from a personal aspect, but no further.

The point is, a name, though important, refers to a person, so it is more important that we are referring to the person (authority, character, power, wisdom, etc) of Jesus, than on how someone pronounces His Name (or what language they use).

A good example of why it is bad to enforce something like this, is what happened when missionaries took the concept of Jesus/Christianity to parts of the world where they knew God by terms that the European missionaries were not familiar with. The local people were afraid to misuse the name of God, and had their own words in their own languages, but the missionaries often would try to force them to use their version of the word "God", the name "Jesus" etc, and thus left the locals in some confusion.

Its surprising that no one said that if you really wanted to render the name accurately in English, you should write Joshua, as that is a more accurate rendition than Jesus. But well, the question is closed and I am too late.

There is absolutely no evidence of an Aramaic original for any of the Gospels, so the safest interpretation is that Greek is the original language for all of them. They don't read like semitic translations, although many Jews were Hellenized by then and many were fluent in Greek and Latin, so it might still have been written by Jews.

The evolution of Christianity is by adding narratives to the septuagint Bible translations, not necessarily by creating translations of new Jewish narratives. The names, as they appear in Greek, are therefore the correct original names, and Jesus is Jesus (or most accurately Ye-sus). In Hebrew, Jesus is translated back from Greek as Ye-Shu, and this is the best redering of the name, since it is a Greek Jewish name, not a Jewish name translated to Greek.

There are those that try to marry biblical narratives to history, and deduce that the Jesus described in the Gospels must have been a Jewish fellow named Joshua. There is no textual evidence for this position, or historical evidence. The best hypothesis is that the stories of Jesus were written in Greek, as original narratives, loosely based on some vague Jewish sect traditions, but mostly based on merging Jewish and Greek traditions into a coherent whole.

The new testament contains as much Greek thinking as Jewish thinking, and it is a mistake to over-Jewify it. It is anti-Leviticus, it is against a literal law-reading of the Bible, and supports an internal spiritual tradition of eternal life, which is mirrored earlier in Plato's philosophy of eternal forms, and is Hellenistic. That some Jews were firmly in the Hellenistic tradition does not make the New Testament Jewish, although much of it is Pauline.

There is no historical reason to view the events depicted in the New Testament historically. Of the new testament figures, basically only Paul is a recognizable historical guy, and perhaps James the Just (who is mentioned by Josephus). Everything else is religious narrative, which is not reliable history, only (mostly) reliable spirituality.

You CANNOT transliterate Jesus' original Hebrew name into English. Since at least one of the Hebrew consonants in this name has no English equivalent. Yeshua is actually a transliteration of the word ישוא, which means "he who brings disaster." It's a little amusing to see "messianic Jews" brag about their knowledge of Jesus' real name. They do not understand that they actually confirm that Jesus has brought disaster to mankind. Has he? Take a look at the history of the last 2,000 years and decide for yourself.