Hello emilmoe,
1) You can’t know who liked it, but you can know count
http://Graph.facebook.com/?id=http://stackoverflow.com
change http://stackoverflow.com with liked site
2) Copy your post link from the address bar.
Go to http://developers.facebook.com/docs/reference/plugins/like/
Paste your link in “URL to like” text box.
Click preview.
You will see the name + photo of your facebook friend in the right
side (Yes, you can see only 2 to 3 friends).
If a person liked your post and not your facebook friend, you can’t find him.
Regards.