Yes thats what I mean.
For example we have a $200 donor - Rainbow (this would be a usergroup) and I want it so all people associated with this usergroup would have the rainbow color?
it seems like this is too much work as I don't have any idea is it possible
But beside that, I don't think it is a good idea to implement it in rainbow colors. Some people find it hard to read that or even disturbing, which would probably make them a little dissatisfied when visiting your site. Does it really require to use a multicolored name? A single color would be much easier, less disturbing for some people and probably overall more satisfying, but that is just my little opinion.
Instead of a rainbow name, just make a user banner with a rainbow color selection (a graphic file) and for the Title something like Rainbow Supporter or use an image before and after the Rainbow Supporter if you just want to have a solid color banner.