Currently util-vserver [0.30.209-2] have no build method "copy", so copying of vserver is some tricky.
There available two useful tools at http://www.micropp.se/vserver/ : vcopy and vrescue.
These tools allows to copy vserver as from local to local, as from local to remote vservers.
Tools not well tested, but its WorksForMe?(tm).
Another variant available for copying/moving a vserver is available under the name [Vserver-Copy]
If you'd like to rename an existing vserver by hand, check out TweakingTheConfig