^ ...father isn't actually his name obviously, this a very simple concept, a name is a label for a person, it doesn't define their identity in and of itself. It was almost certainly father's dream, which means he was either the boy or the homunculus (Pride). People just happen to be confusing cause and effect, father received this name hundreds of years in the past, why can't the present Hohenheim (very closely connected to father) have received the name in some way?
@vemynal, They're almost certainly once the same person.
Hohenheim is almost certainly a homunculus, he is immortal, he's referred to as an it, he bleeds souls/liquid philosphers' stone, and he doubts his own humanity, meanwhile, Mei says that father is definitely human, but not quite, there's something very unnatural about him.
This would of course be because father has expelled/spawned from himself the 7 deadly sins, perhaps he also expelled from himself his humanity, which would have been Hohenheim, this would also fit with the fact that he has abandoned his name and all ties to human society, while Hohenheim sought to live with humans and create a family.