Modern readers can unconsciously hear "Jesus Christ" as though Christ were a family name. In the New Testament, however, "Christ" is a title loaded with Israel's scriptural hopes.
When Peter confesses Jesus as "the Christ," he is identifying him as the Messiah, the Anointed One.
The Greek word Christos means "anointed" and corresponds to the Hebrew concept represented by "Messiah." In Israel's Scriptures, kings and priests could be anointed, and expectations concerning God's future anointed ruler developed in diverse ways in Second Temple Judaism.
There was not one universally detailed messianic checklist shared by every Jewish group. Nevertheless, calling someone "the Christ" was a claim about God's purposes for Israel, kingship, deliverance, and scriptural promise rather than a personal surname.
Restoring the title's meaning gives Gospel confessions their force. "Jesus Christ" means Jesus the Messiah, and statements about whether Jesus is the Christ concern his identity and mission.
It also helps explain why the title could generate both hope and misunderstanding. People could affirm the word "Messiah" while still needing their expectations reshaped by Jesus' teaching about suffering, death, resurrection, and the character of his kingdom.