What is the wisdom behind the Qur’an’s use of multiple phrases when mentioning Jesus, peace be upon him, such as "the Messiah, Jesus, son of Mary," and "Jesus, son of Mary," and "the Messiah, son of Mary," and "Jesus" only, and "son of Mary"? And what is the meaning of the word "Messiah"?

For each mention of the name of Jesus (peace be upon him), whether alone or attributed to his mother, or the exclusive use of one of them, there are wisdoms and benefits. This is likely dependent on the context, situation, elaboration, and conciseness. As for "al-Masih" (the Messiah), it is his noble title, and its origin in Hebrew is "Mashiha," meaning "the blessed."