Namecheap is a good one. I have bought multiple domains, and a couple of hostings before, and I was never asked to verify my identity. I still use them to this day.
But take note their support page state they can ask you to perform identity and payment verification[1].
The same thing applies to Vultr, I never had any issues with them but I did see a couple of users here saying they did ask them for personal info before.
I also recall they require you to use credit card or paypal before you can pay with cryptocurrency.
[1]
https://www.namecheap.com/support/knowledgebase/article.aspx/10520/45/identity-and-payment-verification/