I think rebranding and moving away from Bitcoin is a good idea in general too.
i think that is a good idea since most people here in forum are looking down to altcoins that has a brand of bitcoin, since most people see it as a scam which can hurt bitcore, it wouldn't hurt if they rebrand themselves.
Bitcoin connection isn't quite bad, espacially when we have "bit-'xxx'" pumps (like we had few times in the past f.e when even btcd or btcp was pumped) some people may to get to know about bit-core too.