What exactly happens after I purchased a domain name from you?

Once you submitted your payment or completed the wire transfer process, BestNa.me verifies your payment and contact information. After your payment has been processed, BestNa.me sends you an email containing detailed instructions and the so-called “auth-code”  (also called “auth-id”) of the domain. This is a secret string used by the registrar of your choice to pull the domain to their technical control, and to transfer it to your ownership. After this process of transferring the domain is completed, you will have full control over the settings of the domain via the domain interfaces provided by your registrar.

Notice that it takes several days to complete a domain transfer, regardless of the involved registrars.