Sometimes, perhaps it was simply because they could function as synonymous terms, rather like referring to the current president of the United States by either their name or their role, President.1 Either way, it makes little difference at times.
Although I don’t know of any specific examples, other times, perhaps, the variations were because Paul wanted to make a particular point by using either Jesus’ name or his title, etc. Using the title Christ would remind people of the Old Testament promises about the coming Messiah, the Christ.
1. Christ, technically speaking, isn’t Jesus’ name; it’s his title, his role. Christ means ‘anointed one’ (it’s the Greek version of the Hebrew Messiah) — i.e., the person whom God has chosen for a special role. Jesus is the Christ, he’s God’s specially chosen one who would redeem God’s people and bring in God’s kingdom.