The Y name for Jesus is Yeshua.
Yeshua (יֵשׁוּעַ) is a late form of the Biblical Hebrew name Yehoshua (יְהוֹשֻׁעַ), which is transliterated as Joshua in English. The spelling "Yeshua" appears in the Hebrew Old Testament. It represents a contraction of the earlier theophoric element "Yeho-" to "Yo-" which was common in Late Biblical Hebrew spellings of earlier names.
Therefore, while "Jesus" is the common English rendering, the original Hebrew name associated with Jesus that starts with a "Y" is indeed Yeshua.