I'm assuming that you are referring to forum groups? Lists makes it seem like you're making a database of users and that's it.
I can see why you would want this... IMO, this isn't really needed. Maybe there are some cases that it would be handy, but it would lead to problems (impersonations of highly respected groups, etc.) and personally, I think that not many users would do it. Look around; do you see many people that are part of a group? Not really.
If it was to be implemented, I'd say at least get rid of the trust rating sum thing. I don't see much of a use for it and it could be taken advantage of (a potential scammer finding his way into a group with a high accumulated trust rating, and then using that to scam people without the need to get those DT trust points and wait a while).
Yes, groups would probably be a better term. I'm sure there would be a lot of problems with it, but problems can be solved. I also think almost everyone would use it, much like signatures, if not for themselves for payment. What would be different from the signatures would be that the user creating the group would have some responsibility for it.