@Stephen Britton -

BuddyPress do have a Terms of Service page. Unfortunately, all it says is:Terms

Apologies while we rebuild some bits and bobs. Something compelling will be here shortly.

Ahem. Elsewhere I see others who are using slight modifications of the BuddyPress name making careful note/disclaimer that it is a Registered Trademark of Automattic.

Lesser names can often benefit from 'unauthorized' uses, and may be notably if not studiously lax in notifying trespassers. Trademark language typically uses a 'lynch-pin' phrase such as "no blah-blah, etc, without permission". They can grant case-by-case permission, without compromising their Rights. Worst they can do is say no.

Normally, before seeking such permission, you should have the website available for them to look at (but not public), or at least a detailed & thorough treatment of what you intend, and how you will make sure they will be happy about everything you might do . Or both.

Often, the real concern in cases like these, is not that you might somehow make a dollar off their name, but rather the context or manner in which the protected name will be used (misused, abused, dragged through the dirt, defamed, held up to ridicule, and so on, pretty much endlessly). 'The money' etc is typically not 'the main deal'.

WordPress, BuddyPress etc are mainly worried that bad people will do ugly things, or that otherwise good & intelligent people will do inexplicably brain-dead things, with their trademark name.