Hmm... Initially, I think Sakura would be shocked. She might get confused on how to treat Naruto - after all, he's practically royalty. Sakura is one for treating others with respect and honorifics, and she's always been really casual with Naruto. Naruto? Or Naruto-sama/dono? I'm not saying she would see Naruto in a completely different way, just that she would be confused on how to address him.

But then it'd all settle down and I'm sure Sakura would go back to seeing Naruto as Naruto, just as she always has.

I do wonder if Naruto might want to conceal it once he finds out, at least for a little while. Can't help but think of how Konohamaru was always in the shadow of his famous grandfather for a while. I'm sure Naruto would hate it if people treated him differently just because his father was a hero.