Hmm, I don't recall anybody making this claim, but since so it must be unpopular; here we go.
So we have Luffy who has a Strawhat, given to him by Shanks, yes?
Now even if I want Luffy to gain a new identity different from "Strawhat", I've also imagined that the whole crew would wear Strawhats; they don't have to be the same design but Strawhats all the same. Then they would actually be the Strawhats.