Depends on what you are using the volume for, if it's a lun the vol move command will do it. But if the volume has shares or NFS exports it won't.
It is easy to break a snapmirror and then re-establish it using resync (even if either volume has a different name or is on a different filer). Snapvault, it can be done too but it's not as easy and involves priv set diag / advanced commands.