Hi - Which version of ONTAP are you running? Dependant on the version depends on the method you could use to move the root vol.
If you are using 8.1.x you should be able to use the vol move command. This should perform the cutover as well. If you are using a differenct version you would need to perform the move simialr to other threads on the communities for example: https://communities.netapp.com/thread/23874 or following the KB..
Absolutely. ONTAP doesn't care about the volume name. One caveat I've found to moving the root vol - any shares you have for the current vol0 will have to be manually added to the new vol0. I've been caught out by not having the new vol0 shared root= to my admin host, and having to rewrite /etc/exports with wrfile (unpleasant).