Links to articles promoting the name Yahushua:
“Originally, the name of the Messiah was pronounced Yahushua. This is the Messiah's original name. When the Gentiles tried to transliterate His name into Greek, they came up with ihsoun or "Iesous". When Iesous was transliterated into Latin, it became "Iesus", which was then carried over into English it became our modern day "Jesus" when the letter "J" developed.”
See article in this link (1): http://www.eliyah.com/nameson.htm
According to the article in the link below (2) Yahushua means Yahuwah Saves or Yahuwah’s Salvation and makes this claim:
“While "Jesus" is commonly used to refer to the Son, it is actually from the Greek "Iesus," which refers to the pagan god, Zeus. The name of Yahuwah’s Son is very much like His own: Yahushua.” The article says that the angel Gabriel said the following to Mary: "You will conceive in your womb, and bring forth a Son, and shall call His name Yahushua." (Luke 1:31) Joseph was told the same thing by the angel: "You shall call His name Yahushua for He shall save His people from their sins." (Matthew 1:21)
(2) https://www.worldslastchance.com/why-yahuwah-a-yahushua-only.html
The notion that the name Jesus means “Hail Zeus” is refuted in this link (3). The article explains how some who say the name of God is YAH, then conclude that the Messiah’s name is YAHSHUA (meaning “YAH Is Salvation”). Part of the article says:
“They contend that is the name used by the apostles and by the Messiah Himself; however, after the apostles were dead and gone, the Roman Church took over Christianity. In order to make their brand of religion more palatable to the pagans, the Roman leaders changed the name of the Messiah into a Greek/Latin hybrid, Iésous, which (supposedly) means “Hail, Zeus.” Since Zeus (or Jupiter) was the chief god in the Greco-Roman pantheon, the pagans had little trouble accepting this new demigod. By changing the Savior’s name, Christianity had been effectively stripped of its Hebrew roots, and the melding with paganism was a success.... the Messiah’s Hebrew name is Yeshua, not Yahshua—the latter being a fabrication in order to make the name sound more like YAH.”
(3) https://www.gotquestions.org/Jesus-Hail-Zeus.html
Finally, an article I found on the Sacred Name Movement (4) illustrates the futility of insisting that one name, and one name alone, is the right name for the Messiah:
“Further, not even the adherents of the Sacred Name Movement can completely agree on what the sacred names actually are. While “Yahweh” and “Yahshua” are the most common, some propose “Yahvah,” “Yahwah,” “Yohwah,” or” Yahowah” for God and “Yeshua” or “Yahoshua” for Jesus. If there is only one non-blasphemous name each for God and Jesus, we better be sure to get it right.”
(4) https://www.gotquestions.org/Sacred-Name-Movement.html
The basis for the belief that the name of the Messiah is יָהוּשׁוּעַ (Yahushua) continues to elude me although Deek's answer is intruiging.