How can I find that buyers what products they have purchased

Are you using a plugin such as WooCommerce for this? What theme are you using? Could you please provide a link to your site so we can get a better idea?

Yes I Use from WooCommerce
My theme :AccessPress Store
My Site : Theprogrammer.ir

I would recommend asking on the WooCommerce support forums, where the developers and others already using the plugin may be more likely to see this.

I have also moved this thread to the Plugins and Hacks forum.