The way to track referrals is described in the "Like" button documentation:
http://developers.facebook.com/docs/reference/plugins/like/
If you provided "ref" parameter then facebook will add two parameters in the URL to your site:
Is there any way to configure what are URL parameter names that facebook will use to pass these data?
The reason I would like to change that is to have same "ref" parameter name for all social networks (I didn't investigate, but some other social networks could have different parameter name and I don't really like idea to support whole variety of them).
Any feedback is very welcome!
No, there's no way to change this - you'll have to either log each network separately, or just hard-code those values in for Facebook and use ref= elsewhere