Birmingham used the citys name and villa didnt. Villa are by far the bigger club and bigger name in football. Nothing to do with badges, Icons or naming rights...it's success that produces recognition. We have had none for decades. We have to become a more succesful club to earn that....a bird on a crest (at this moment in time) would be moot.
Success + Good Marketing
Even in successful periods in our history, on field success was never matched by off field marketing acumen.
That is why despite being as successful and glamourous as most in the 60s when the TV boom began we fell behind our neighbours in self promotion and it is why when the Sky/EPL era began, when we were still among the clubs most likely to succeed, we were left miles behind United and Arsenal, whom up to that point had won no more league titles than us.
If and when we become successful again, that must change so that so that we do indeed produce more recognition in this modern era.