It was in Antioch that the disciples first got the name of Christians. (REB)
This is Luke’s very benign statement.
It doesn’t tell us, or how, only that the Antiochenes called the followers of Jesus ‘Christians’ first.
It is a parenthetical, a footnote — not a linear event. Nor does it tell us when the sect adopted the name of Christians for themselves.
You cannot convert to something that is not separate.