Who gave Angel his name?

Question

Revealed in Season I "The Prodigal"

Not, Angelus or his birthname, but the name Angel.

Answer 1

Technically, he gave it to himself. When he was turned into a vampire, he named himself "Angelus" because his little sister thought he was an angel when he came back to slaughter his family. When he got back his soul, he changed his name to "Angel" to distance himself from his previous soulless self. So while both "Angelus" and "Angel" were inspired by his little sister, Angel was the one who decided in both instances what name he wanted to be known by.