Handed down from Jeff, I Give You My Name can both bow and destroy its own caster to pay its cost.
Design Team and Rules Junta is looking into making a clear template for costs to distinguish those that must be paid by two cards from those that can be paid by two cards or one card. That new template still won't retroactively apply to I Give You My Name, so just run with it.
Have fun with your big stompy monsters, folks.
- Marty Lund
Deputy Rules Monkey