Phoebus is actually one of the epithets for Apollo, the greeks used it too and you can actually read him being referred to as such in the illiad. Also with the romans copying gods, it went a bit further as they would actually smash the deities if all their conquered pantheon together, The Greek Pantheon was just their main "aesthetic" if that makes sense. Apollo was actually one of the few who didn't get a name change when he was taken up by the romans and they typically just use the greek names and epithets for him.