The problem isn't the Flight's name. The RAF sees the BoB as its major historical asset, its USP if you like. By presenting itself in this way it automatically triggers a positive response in the public's mind. Anything that reminds people of the Bombing Offensive for instance would have the opposite effect (or that at least is how I assume the thinking goes).
This conundrum is purely of the RAF's making. It has never stood by Bomber Command, nor in particular its Memorial in London. It took a Bee Gee to push for that, the RAF establishment only associating itself with it when it became a done deal. That is why you are stuck with the RAF BBMF.
Embrace it, you know it makes sense!