I have an ExUM server that I must relocate. To maintain consistency with standards, I must rename this server. Can I rename this server, or should I remove the UM role from it and bring it up as a new UM server with its new name?

You've never been able to rename Exchange servers in the past and that's true with E2K7 roles like Mailbox, etc. I've not heard anything differently for the UM role. Here's a guide from MS on moving the role to new hardware and maintaining the same name: http://technet.microsoft.com/en-us/library/bb332344(EXCHG.80).aspx