The name ‘Jesus’ (‘Jeez-us’ in English, ‘Haysoos’ in Spanish) is the Anglicization of the Latinization (‘Iesus’) of the Hellenization (‘Iesous’) of the Aramaic form (western ‘Yeshu’ or eastern ‘Isho’) of the later form (‘Yeshua’) of the Hebrew name ‘Yehoshua’.
‘Jason’, or ‘Iason’, by the way, is another, more rare, Hellenization of ‘Yehoshua’, for which another Anglicization is ‘Joshua’.
We know that the protagonist of the gospels was not a White American, much as the American Christian Right would like to believe, so we can be sure the name of the actual person was not and never was ‘Jeez-us’. Not being Latino, he would not have born ‘Haysoos’ as a name either.
‘Iesus’ would only have been a possibility if he were living in the west of the Empire, and since he was not, that is out too.
In many ways, Galilee was more Hellenized and cosmopolitan than Judea, though probably not as much as Samaria, and Greek was probably spoken as much as Aramaic. Therefore the Hellenized version of his name may have actually been the one used on a day-to-day basis; several of the Twelve, for instance, have purely Greek names (Andrew, Philip, Peter).
Messianic Jews, many evangelical Christians, and the increasing number of Jews who consider him to be a prophet favor the later form ‘Yeshua’. This was the same used in later years in Palestine, though in the final two centuries of the Temple era, the older ‘Yehoshua’ began making a comeback, particularly in Galilee.
The Talmud, in sections which are decidedly non-complimentary, uses the West Aramaic form ‘Yeshu’. This would be fine were West Aramaic the form spoken in first century Galilee, but, alas, it was not; their dialect was close to the East Aramaic of Babylon.
Muslims, by the way, use the form ‘Issa’, and yes, they hold him as a prophet.
The Assyrians, Christians of Middle Eastern churches which used Aramaic or Syriac as their liturgical, and sometimes spoken, language use the name ‘Isho’.
Marcion of Sinope’s gospel the Evangelikon, as well as his Apostolikon containing ten Pauline epistles, referred to its protagonist as ‘Isu Chrestos’, or perhaps ‘Iso Xrestos’. Besides the witness of Tertullian of Carthage, writing in Latin, we do have a fair number of inscriptions with the name carved into them.
Since we have these, and since Marcion and his sect, which lasted at least into the fourth century, are less likely to have been tampered with by interpolators, redactors, and pious fraudsters, my bet would be that their version is closer to the actual name. Given that Marcion, being wealthy and educated, would certainly have been familiar with ‘Iesous’ as the Greek equivalent of ‘Yeshua’, the most like original name was ‘Isho’.
That would render the forms Isho Teeb, rather than ‘Iso (or Iesous) Chrestos’, and Isho Meshiha, rather than ‘Iso (or Iesous) Christos’.