@robin-w, I think bbPress does just what you’re saying. But (if I understand things correctly) BuddyPress will change the WP “display name” (and/or “nickname” ???) when you update your name in the BP profile — If “synching” is on. I use BP, but I actually have synching OFF, so I’m not all that familiar with the details.
BTW, the same goes for email. You can change that in the BP profile too, and (if allowed) it updates it in WordPress.