Running rsync as root: Operations Not Permitted

It's because the target is on a mounted network volume. You're running rsync as root, but that only gives you permissions to change ownership on the local (client) computer -- as far as the file server is concerned, you're whatever user authenticated to it, i.e. not root (unless you're using NFS, in which case it's more complicated). Since you're authenticated to the server as a normal user, all files you create on the server will be owned by that normal user, and you won't have permissions to change that.

I see two possible solutions:

• Don't try to set ownership on the server. Use rsync -rltgoDv ... instead of rsync -av .... -a is equivalent to -rlptgoD; leaving off the -p means it won't try to set ownership on the target files, it'll just store them all as the current (authenticated to server) user.

• If you really need to preserve ownership (and your local accounts are the same as those on the server), run rsync over SSH instead of file sharing, and SSH into the server as root. Something like rsync -av ... root@server:/Backup/$name\ -\ $(date +%m-%d-%y) ...

  Note that allowing root SSH into a server is generally a bad idea. If you want to do it this way, I'd create an SSH public/private key pair (with an encrypted private key), use that for authentication, and configure the server to reject password-based SSH authentication (at least for root).