Can you imagine that FB sells this information anywhere in the near future? I bet they can make great profiles of you, and compared to a big pile of people with similar profiles, the bank can see what profiles predict risk.
http://33bits.org/2011/03/09/link-prediction-by-de-anonymiza...
As the site name implies, you need just 33 bits of good information to distinguish every person on Earth. It's not hard to get enough bits from your Facebook timeline to cross-correlate it with other stuff the bank might know about you.
2) Let's not forget they have more than your name. They can geolocate your IP, for example, to get an approximate location. If I remember correctly, name and zip alone has something like an 85% chance of uniquely identifying someone. If you tell them your birthday, that chance goes up into the high 90s.
3) Once you have their cookie, they have many other sources of information thanks to "beacon"[1]. Identification becomes significantly easier when they have other businesses adding data.
It must be nice to have a common name.
The only ways in which this can work is a) you have a pretty unique name on FB or b) you have to give your FB name on your credit application (if I'd see this on a form, I'd just tell the bank guy to forget everything and walk out).
Of course, this opens a possibility for manipulation - either you use someone else's clean FB page, or a malevolent entity creates a profile in your name, or you yourself have one "clean" profile and one "real" profile which many people already do to hide their pot smoke pics from potential employers.