Hello, does it have anything to do with Coinbase (the company)?
You mention that it's self-custodial. Does it require a coinbase account?
Finally, what makes it unique?
Wind_FURY answered your questions. You should also know that Coinbase wallet is closed-source. So, if you don't like it because of its name and the support it has for Ledger hardware wallets, there is now a third reason why you should stay away from it: its closed-source nature. Who knows what's going on in the background and what happens to your keys.