're-' originates from Latin, where 're-' meant 'again' or 'back', combined with 'baptize' which ultimately derives from Greek 'baptizein' meaning 'to dip' or 'to immerse'.

're-baptize' is formed from the modern English prefix 're-' + 'baptize'. 'Baptize' came into English via Late Latin 'baptizare' and Old French 'baptiser', from Greek 'baptizein'; the construction with the prefix 're-' follows regular English word-formation patterns to indicate repetition.

Initially, the root meant 'to dip or immerse'; in Christian usage it came to mean 'to perform the sacrament of baptism', and 're-baptize' specifically evolved to mean 'to baptize again' (or, figuratively, to give a new designation).