Wait, if the Original Family's surname is Mikaelson, then why Elijah is a Smith ?

Elijah's last name isn't really Smith. He just made that up when he pretended to be a journalist o autor o whatever it was. I'm assuming Mikaelson isn't the family's real last name either. 'Mikaelson' probably comes from 'sons of Mikael' because that's what their dad's name was. At least that's what I'm thinking. Hope I helped :)