Hello everyone,

I'm looking for a certain scenario, perhaps someone has an idea.
Protagonist A becomes buddy buddy with person B, perhaps even falls in love with this person. Some time later A finds out that B is actually a very prominent person. A now treats B with the expected respect while B isn't happy about that at all. From here on the story progresses while those two try to overcome their social boundaries.

I'm aware that this isn't exactly an original story outline, perhaps there is even a name for it.

I don't think most of these fit exactly. They are kind of like the plot you described. I put them under a spoiler tag because it's a surprise in many of them.

Basara - they are both prominent people with secret identities. They are supposed to hate each other.
Skip Beat! - It hasn't really been resolved (she doesn't know yet), but I assume it will eventually have to be resolved.
Kuragehime
Twelve Nights
Ghost Hunt
Kanata Kara
Lapis Lazuli no Oukan - this one is actually pretty close to your description.
Orange Marmalade - it's not that she's famous, it's just a big secret that she's keeping. There is a lot about the resolution.
Song of the Long March - might fit. The main character is secretly a princess seeking revenge, but there isn't much of an issue about it with her love interest.