At this time, VMs cannot be renamed by customers.

If you've just created the VM and haven't put much work into configuring it, the best option is probably to delete the VM and recreate it with the desired name.

If you've put work into the VM and don't want to delete it, you can request that the UT-VMG administrators rename the VM and update the DNS records. Renaming the guest OS is the customer's responsibility, but UT-VMG administrators can change the display name and update DNS records as long as the DNS zone is delegated to UT-VMG. If the DNS zone falls outside of what is delegated, then it's the customer's responsibility to manage changes. Check KB0014268 - DNS Questions for more information. 

Send the request with the current VM name and the desired new name to utvmg-support@austin.utexas.edu or contact the ITS Help Desk.