Lol, maybe Han was also a fan of podracing.
If he did really have a middle name, I would guess that it would be Organa. I would think Leia would still want to carry on the family name of the Royal House of Alderaan.
Speaking of which, I always liked the idea that Kylo Ren was sort of a “dark prince”, since he would have some claim to the throne of Alderaan. I could imagine citizens of the galaxy whispering amongst themselves one of his nicknames, Prince of Ashes.