Who gives Paul the name Magnus Eisengrim, or does he rename himself? Also how does this name change represent his rebirth?

I believe Paul names himself this. Paul takes what Dunstan teaches him (magic) and later re-invents himself, first as a carnival performer and then as world-famous magician Magnus Eisengrim. Like Dunstan and Percy, Paul becomes a new person, and yet remains tied to the childhood feelings (of resentment and insecurity) that plagued him as a child. His transition into magic is a baptism of sorts but he still remains tied to his past.