You don't want Wendy's to be impersonating McDonald's, and making questionable claims. For Wendy's, the name "Wendy's" is their real name. Wendy's Incorporated.
Likewise, "Projekt Melody" is the real name of intellectual property being presented as a speaking entity, even if it is owned by a parent company.
A business' real name is their name.
You don't want Wendy's to be impersonating McDonald's, and making questionable claims. For Wendy's, the name "Wendy's" is their real name. Wendy's Incorporated.
Likewise, "Projekt Melody" is the real name of intellectual property being presented as a speaking entity, even if it is owned by a parent company.
Don't see any issues there.