The name of the Messiah, in Hebrew-his own language, is Yahshua (Hebrew), which means "Yahweh is salvation" or "Yahweh saves". The name "Jesus" is the result of a series of changes from Hebrew to a Latinized Greek. The word is not a transliteration, and it cannot be translated, since it is a hybrid word.

Hebrew names can be translated; they make a statement, such as, Yahshua = "Yahweh is salvation". The word "Jesus" does not deliver the message that Yahweh is salvation. [and, of course, "Jesus" was never actually his name.]

The pronunciation of Yahshua (Hebrew) varies among different groups.  Since the Hebrew spelling is exactly the same as "Joshua", the son of Nun, some people pronounce it as "Joshua" with a "Y" sound - Yahshua; the "Y" would be the correct sound since the "J" sound does not exist in Hebrew.  In fact, because of the same spelling, the King James Version mistranslated Acts 7:45 and Hebrews 4:8 using "Jesus" instead of "Joshua" (other versions like the NIV have corrected this).  In reality, the name of Joshua and the name of the Messiah were the same name.

Stong's Concordance states that #2424 - Iesous is of Hebrew origin #3091 - yeh-ho shoo'-ah; and that this is also the name of Joshua, the Jewish leader.  Some people state that the ancient pronunciation of this name is Ya-HO-shu-wa, and that by the time of the Messiah, the "HO" had been dropped; I have seen no written study of this.  Strong's has obvious errors, "Yeh" instead of "Yah." His vowel points are of more modern Hebrew usage; he uses a sheva instead of a pattach and thus gets "Yeh." And, he uses "Jehovah" instead of "Yahweh."
We can understand, now, that "Jesus" would not have been the name that Miriam (Mary) was told to give her son. The "J" sound didn't exist then, and doesn't exist now, in the Hebrew or Aramaic languages. In fact, it didn't exist in English until 500 years ago.

"Yeshua" is the name used by today's Jews and messianic believers when referring to the Messiah.  The "Ye" was a replacement of "Yah" to avoid pronouncing the Father's name even in its shortened, poetic form [a traditional Jewish restriction that began at the time of the Babylonian exile]. Using Yeshua does not honor Yahweh as intended in Matthew 1:21 above. By pronouncing Yahshua, we state that Yahweh is salvation.

It is to be expected that people would have slightly different pronunciations, but the "Yah" portion of the name is well documented.  An honest attempt to pronounce this Hebrew name from the Hebrew letters shows respect to the Messiah and to Yahweh, even if we may not be saying it quite correctly.  This is more respectful than replacing the name with something else that is not a translation or a transliteration.