Okay so one of my character's mom is from Japan and his father is from my fantasy world so how exactly would their last names work? In my world they have the more western format and in Japan they have more formal ways of referring to people so how would it change or would it change at all? Does it depend on family dynamics or something else? I don't know if this is a weird way to explain things but if anyone could direct me somewhere that would be amazing
BehindTheName is usually reliable: https://surnames.behindthename.com/names/usage/japanese
If they live in the mundane world (not fantasy world) and the father's documentation isn't existent or admissable, then I suspect it can work the same way as a lower-class man taking on the family name of a higher-class woman during marriage and the children from that union inherit the family name from the mother rather than the father.
Unless you're asking if Dad from Fantasyland becomes Fantasyland-san, or if the mother becomes Mrs. Mori or Mrs. Uehara or Mrs. Fantasyland…
Both can happen depending on how Westernized or Easternized the speaker wants to sound. Maybe Dad from Fantasyland's brother-in-law wants to show off language fluency, then will call him Mr. Fantasyland and even call his own sister Mrs. Fantasyland. But if the great-grandmother-in-law is very traditional and looks down on gaijin, and Dad from Fantasyland wants her to like him, then I think Dad from Fantasyland is going to take being called -san.