It seems like when you want to play in multiplayer. PPD only use folder names to determine if you've got the song chosen by the "room master". But if two people have the song, but one of theses changed the name folder, PPD doesn't recognize the song.
Is it possible to fix this please?

No, PPDMulti doesn't recognize songs by "Folder Name" but hash of score file(*.ppd)
So, if you are said "you don't have score", it is because the hash is not matched in all score which you have.
You can resolve this by updating scores.