Why is there a difference between the names of prophets in christianity, islam and Judaism, for example we refer to Jesus (AS) as Isa(AS).
How did this difference occur and why?
A name is a name no matter which language it is!
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The origin of the name of 'Isa (peace be upon him)
Well according to Arabic Wikipedia the original name of Jesus or 'isa (peace be upon him) is derived from Aramaic (which looks like Muhammad in Arabic) to hebrew and it's pronounced Yasho' يشوع this is a combined name from two different words Yehwa sho' يهوه شوع (Yehoshua)which means God/Allah/Yehowa rescues or is salvation.
This name was well known and widely used among Jewish people (Banu Israil) many (examples) of them are mentioned in the old Testament one of them was Yosha' bin Noun يشوع بن نون (Joshua) who followed Moses (peace be upon them) in leading the 12 leaders of the Banu Israel (read for example (2:60 or (5:12)...).
The origin of the name used by Christians
The origin of the name used by Muslims Some say that Arabs and the Qur'an used the name 'Isa عيسى instead of Yosa' or Yosha' is a kind of translation into Arabic (similar to the Greek version).
Here some more details and Information beyond Arabic Wikipedia:
Some more details in Arabic could be found in this Fatwa or in this Arabic site which claims that the Aramaic original is more likely to be pronounced 'Isu عيسو or 'Isa عيسى and as Greeks don't have a letter for "Ayn عين "ع" they toke 'Isus "عيسوس" as an origin for "Iyesus".
And Allah knows best!
Whenever a prophet comes...he speaks to the people with their own language. A prophet can't go to Russia and then start giving them a book with Arabic and address them with the language and dialect of Arabic. As in the Quran Allah says:
وَمَا أَرْسَلْنَا مِن رَّسُولٍ إِلاَّ بِلِسَانِ قَوْمِهِ لِيُبَيِّنَ لَهُمْ
And We did not send any messenger except [speaking] in the language of his people to state clearly for them
So if a prophet goes he has to speak with their language and dialect e.g. from this link we have:
Moses (/ˈmoʊzɪz, -zɪs/; Hebrew: מֹשֶׁה, Modern Moshe Tiberian Mōšéh ISO 259-3 Moše; Syriac: ܡܘܫܐ Moushe; Arabic: موسى Mūsā; Greek: Mωϋσῆς Mōÿsēs in both the Septuagint and the New Testament) is a prophet in Abrahamic religions.
Even right now if you go to two different states of a country, you see them having slightly different dialects... imagine how all that could change by time, location, or language...
One last note is that the names from different languages all share a similar way of saying... in Arabic we Say Musa... in English they say Moses... its not they are saying Jack... Or we are saying Ya'cub... they are saying Jacob.