He's not The Doctor from Doctor Who
He's from an UT AU I've created where Frisk is a timelord. So Frisk is the Doctor.
He's already regenerated once, which is why he has the current face and not Frisk's face
And for the OP, he regenerates when he dies, gaining a new face, and a new personality (but generally same morals if that makes sense? As in, still a good guy and tries to save/help as many people as possible and not to kill anybody or anything).