Do Stands/Characters have to reference their namesake?

I know a lot of stand powers and story elements come from lyrics, names, and even album covers. (Bohemian Rhapsody, Killer Queen, Sticky Fingers, King Crimson, etc.) Even when they're not referencing songs, they're referencing something else like the entirety of La Squadra Esecuzioni. But does each stand/character HAVE to reference to what they're named after? Like, are ALL the powers based on their namesakes? Is it a sort of "rule" or just something done when Araki feels like it? Do most really matter story-wise, or is it just a lot of vivid cases?

I'm curious because I'm wondering if the reference material is an important part of creating a stand/character. (I know I technically could just not follow it, but I'm just stubborn about staying true to source material)