Why do you need to buy anonymously? Theres anything wrong if they know your name? Maybe you are doing a wrong thing so that you want to buy or sell anonymously.
there is actually a probleim in sending your persona ID, if the exchange will be hacked one day(pretty common nowadays) then the hacker can steal your identity and use it for criminal stuff
this is why many don't want to deal with exchange that require your id
So that the reason why do you need to buy anonymously? If no one will gave their identity in different exchanger or what ever that needs ID what will happened to that country?