I like the initiative but I have never quite understood why would any company use the word "Remix" in product they try to market. To me at least it looks very unprofessional and downright childish; business isn't good either in this context. I would go with similar naming to SEL and RHEL:
Ubuntu Enterprise Linux (UEL)
Ubuntu Enterprise Edition (UEE)
Ubuntu Enteprise Desktop (UED)
...or something like that.