ENS names were rage last few years. And each blockchain is coming up with their own. Be it btc, eth, solana, and many others are on the lineup with the ENS naming system. So it's going to get easier as the basenames are going to get attached to the wallets. 

These names would be easy to claim as the base offers initial pricing but after that it would go down in 24 hours. And it would be opening doors outside the invite only pages. So you should check things out as well. 

You can access this through wallets or the coinbase account too. Then you can apply for the domain search and then you would be presented with page like this as well. I tried searching for name for myself and came across this but disappointed as it did not have .base or .eth instead it was like base.etch. 

So on that note kind of disappointed with the long name. 

Base blockchain is promoting the ENS as of now. And in near future more things would be coming up in the market. And hopefully things get better as the prices of such address and easy to renew and updates process would be out for us soon enough. 

If you wish to get the on chain identity for yourself then this does makes sense. But long term I feel like there needs to be better domains. Like .base would be a good extension and .eth is already good enough. 

Have you tried the base.eth names?