In the Quran the 'Messiah' is a title that belongs to one special person. In fact the Quran uses the word Messiah and only applies it to Jesus, but not only as a title but even as Jesus' own personal and proper name:
The Angels said, “O Mary, God gives you good news of a Word from Him. HIS NAME IS the Messiah, Jesus, son of Mary, well-esteemed in this world and the next, and one of the nearest. 3:45
They have taken their rabbis and their priests as lords instead of God, as well as the Messiah son of Mary. Although they were commanded to worship none but The One God. There is no god except He. Glory be to Him; High above what they associate with Him. 9:31
However Biblical Scholar Bart Erhman explains why this is wrong:
"The single most common descriptive title that was applied to Jesus in the early years of the Christian movement was the term Christ. Sometimes I have to tell my students that Christ was not Jesus’s last name. Most people at the time Jesus lived, apart from the upper-crust Roman elite, did not have last names, so he was not Jesus Christ, born to Joseph and Mary Christ. Christ is a title and is, in fact, the Greek translation of the Hebrew word for messiah. Saying Jesus Christ means saying Jesus is the messiah."
[Bart D. Ehrman. HOW JESUS BECAME GOD: The Exaltation of a Jewish Preacher from Galilee, Kindle Edition (San Francisco, CA: HarperCollins, 2014.) p. 100]