Of course not but there is a catch. The name Jesus didn't even exist until the English translations of the 18th century when the letter j came into being replacing the Y sound. This means Joshua also would be a late comer, so Yeshua or its derivatives would still be the best bet if one wanted to keep it proper. Would calling someone of a foreign name Bob be representative of their name?
That’s fairly spectacularly inaccurate. The word originated in Latin as the translation of the Greek Iesous, which historically lacked a J character, as Iesus, and from there spread to other European languages including the Romance languages and Germanic languages, including English.
The first use of the specific spelling with a J instead of an I in the English language dates from 1532, in the 16th century, not the 18th century, and the spelling became definitive in 1629 when J became recognized as a discrete letter for producing the soft g sound, but the word already existed - the fact that one of the typographic glyphs used to pronounce it phonetically has changed is irrelevant, since these glyphs have changed repeatedly over time. For example, the sound th used to be made using a lost letter of the English alphabet called a Thorn, which Icelandic still has, and which I wish we could recover. W, U and J are all fairly recent glyphs. Thus historically, to make the sound Jesus, one would have written IESVS .
The first use of the Latin form of the name of our Lord, which had the sound of “Jesus” was in the 1st century, among the Latin=speaking people of the Western Empire such as the Roman soldiers and Pontius Pilate, and in the inscription above His cross “INRI” the I stands for Jesus, and this was the pronunciation used by Latin=speaking Christians from the beginning (the Bible and liturgy were translated from Latin to Greek in the 2nd century in order to be accessible to Romans not lucky enough to be born into wealthy families who were sent to the Grammaticus and Rhaetor to learn Greek, and in the fourth century the Vulgate made it accessible once more, since the vernacular form of the language had deteriorated from the classical Latin of the second century Bible, the Vetus Latina, but some phrases from the Vetus Latina survive even today, such as “Gloria in Exclesis Deo.”
Now regarding referring to our Lord as Joshua, while it is true that this is the Hebrew version of His name, at the time He was born, Hebrew was not in use as the vernacular language of the Jews, but had been superseded except in religious liturgical contexts by Aramaic, and even in the religious sphere Aramaic had made substantial intrusions, in that Aramaic words became ubiquitous in the old Testament (there is at least one in Genesis), and some entire books of great importance such as Daniel were written in Old Testament Aramaic from the start. Additionally, the Bible and Hebrew were written using a 22 letter subset of the Imperial Aramaic “square letter” alphabet, which replaced the Paleo-Hebrew alphabet among the Jews (but not the Samaritans, who continued to use the old style of writing and who use a script derived from it to this day). Thus our Lord was referred to in Galilean Neo-Aramaic as something like “Yeshua”, which in later Syriac dialects was simplified, becoming Isha in the Eastern accent of Classical Syriac and in the Neo-Assyrian Eastern Neo-Aramaic dialect which is spoken by just under a million Christians of the Assyrian Church of the East and the Ancient Church of the East, remaining the largest surviving Aramaic speaking population. There are other Aramaic speaking popualtions in the Syriac Orthodox Church (Turoyo survives among some Syriac Orthodox from Turkey, and another dialect among those living in Jerusalem and Bethlehem) and the Antiochian Orthodox Church (the village of Maaloula in Syria, which was occupied for nine months by ISIS, speaks Aramaic and has a convent of Aramaic-speaking nuns.
There are also some non-Christian speakers, such as the Mandaeans (who believe themselves to be followers of John the Baptist, but are in fact the last surviving Gnostic sect) whose Classical Mandaic language is somewhere in between Classical Syriac Aramaic and the Neo-Aramaic used by the Talmudic
geonim of Judaism in Seleucia-Cstesiphon.
