You have plenty of exchanges that do not ask for ID verification, and some of the most "trusted" ones, if you can actually really trust an exchange, have already been pointed out by some users. The problem in my opinion, is that as regulation of crypto takes place, I'm pretty sure all exchanges running with a license will have to comply with KYC regulations. That's the norm in financial services to somewhat help prevent, or at least make money laundry more difficult. So these exchanges will probably ask for ID in the future or close doors in my opinion, so you should still be careful with them.