Or, the call out to the Valleyard, could be a hint to us, that HurtDoctor is a Spinoff incarnation (Like the Valleyard and the Dreamlord), not an actual Regeneration, meaning a Regeneration wasn't used up making HurtDoctor. We just don't know until we see HurtDoctor's story play out in the Anniversary Special. Maybe that's the biggest reason Smith feels righteous in denying him the use of the name, because he's not a real Regeneration, he's a manifestation in some way. And yea, he may be everything the ending of NotD led us to believe (A previous Regeneration that he's ashamed of and has disowned and disavowed)
Yes, right now, it seems safe to assume HurtDoctor used up one of The Doctor's 13 lives, but you know what happens when you ass u me