I think that people in FTL/EF don’t have last names. But when Regina made a coffin for her father here, she had to put a last name on it so she just used the same one she’d chosen for herself to have in SB.
That’s right. Last names are a relatively recent invention of Western culture. Cora’s husband Henry had no last name. So when Regina (Or the curse? Or the writers?) needed a last name for her life in Storybrooke, she (Or it. Or they.) just chose “Mills” because of her connection to a miller.