Can I assign a new client address to an existing BNS name?

Yes you can. If you use MetaMask to manage the BNS name, you can go to the Diode Network Explorer’s BNS page and simply enter a new Client Address / ID in the box provided under the BNS name. You must be authenticated with MetaMask and connected to the account that owns the BNS name.

You can use the Diode Client to do this without MetaMask per:

diode bns -register <name>=<new_address>

In order to run this command, the Diode Client running the command must be the original owner of the BNS name.