Why would the Jewish sages (who don't believe that the messiah will suffer and die), in Talmud Sanhedrin 98b, link the name of the Messiah to Isaiah 53:4, where the context talked about someone that suffered and died?
Apropos the Messiah, the Gemara asks: What is his name? The school of Rabbi Sheila says: Shiloh is his name, as it is stated: “Until when Shiloh shall come” (Genesis 49:10). The school of Rabbi Yannai says: Yinnon is his name, as it is stated: “May his name endure forever; may his name continue [yinnon] as long as the sun; and may men bless themselves by him” (Psalms 72:17). The school of Rabbi Ḥanina says: Ḥanina is his name, as it is stated: “For I will show you no favor [ḥanina]” (Jeremiah 16:13). And some say that Menaḥem ben Ḥizkiyya is his name, as it is stated: “Because the comforter [menaḥem] that should relieve my soul is far from me” (Lamentations 1:16). And the Rabbis say: The leper of the house of Rabbi Yehuda HaNasi is his name, as it is stated: “Indeed our illnesses he did bear and our pains he endured; yet we did esteem him injured, stricken by God, and afflicted” (Isaiah 53:4).