Digital identity based domains are out since the Ethereum name service being deployed. Like say ENS was deployed since a long time. You can now map the Ethereum wallet to the domain name. Later this was used by other blockchains like Bitcoin Cash, Solana, and now even the Bitcoin. There are some of the companies who are into this space already. Namely Hiro, Trust machines and few others. 

Recently they got the funding to the project that is already working into the bitcoin based name service. Trust machines being the bitcoin layer 2 company they recently posted about the web3 identity solution named Orange Domains.

Web3 domains are going to act like a NFT token. And you would be buying and holding it like that. You can also transfer it to another person or the system. Where the new change is the system is on the layer 2. Where you can create smart contract, new features and also the emails, finances movement in the orange domains. Tucows has also helped launch the orange domains. 

.BTC domains have been registered through the Hiro and Trust machines. So the orange domains would be the leading place where the domains can be registered and also the btc based assets can be there for the hosting. Some of the time it can be pretty good for the wallet to have the domain names like this. Which would save you from giving your address to others or even the lightning network like URL too. 

You can check out the Orange Domains.