A few months ago, I thought about a bbPress fork from bbP 1.0.x, which I had called bbDiet. After a few days considering the fork, I found that I am not able to do it alone, and my current engagement in bbP (I do the only german translation of the current release and maintain a website about bbP in german language) will be abandoned if bbP is converted in a WP plugin.
But a really good replacement should stop walking in that dead end called BackPress, and the name of it should not sound like "being always a little hungry while using it", as the word "diet" suggests. A good replacement is a minimalistic system with a rich selection of plugins, allowing it to be whatever is wanted for a specific project. It is better forked from the great bbP 0.9.x, which was faster and needs less resources and MySQL queries on the server's side.
Perhaps a recursive acronyme, choosen in a way that it is pronouncible in most languages is a better name, something like BINABB (Binabb Is Not A Bloatware Board) or EMFESAG (Emfesag Means: Fast, Extensible, Simple And Great)...