Jesus, the man, was Hebrew and the name given to him would be Hebrew.
Act 4:10 Be it known unto you all, and to all the people of Israel, that by the name of Jesus*(G2424) Christ of Nazareth, whom ye crucified, whom God raised from the dead, even by him doth this man stand here before you whole.
G2424
Ἰησοῦς
Iēsous
ee-ay-sooce'
Of Hebrew origin [H3091]; Jesus (that is, Jehoshua), the name of our Lord and two (three) other Israelites:
Act 4:11 This is the stone which was set at nought of you builders, which is become the head of the corner.
Act 4:12 Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.
I was, at one time, stationed in Germany and during that time the Germans called me by my given English, name. I feel we should do the same when speaking of our Lord. After all, it is the name by which we must be saved.