回複：is suing FBI for name check a good idea?

If you are serious about this, check out
http://boards.immigrationportal.com

You will need to file something called
"Writ of Mandamus", it's kind of tricky since you have to show you have exhausted all "administrative remedies", such as contacting FBI, USCIS, Senator, Congressman, whitehouse, etc. But it can be done and there are sample/template you can modify.