Naming rights of my cat – as NFT

I'm thinking of a project but don't want to get too in to the specifics so here is a similar idea:

I want to sell the naming rights of my pet cat. Whoever owns the token can change the name. I'll check the token each morning to see what I need to call my cat, as its name may have changed (ideally it can only change once per ownership but this isn't a necessity).

How can I do this? I know I could mint an NFT – but I'd want to be able to have a link so I can check the name – so there'd need to be some editability of it and only by the owner of it. Whatsmycatsnametoday.com could look it up for example and display it.

What's the simplest way for this to work?