Not all people go through the problem of the name check. If you are just beginning the process is a waste of time to worry about something that you can't control or if you have no idea if you will be in it. If you get in that situation (in the interview you will know) and you have been waiting a long time I think is better to contact your congressman IF that helps but normally they don't have overpower of security issues like this.
Check around this forum about "FBI name check" and you will get an idea. The FBI make a search with your name and date of birth (is not your FP). That takes time (normally occurs during your pending application of I-485) and if your name (including alias) comes with a "hint" means that somebody with your same name has committed a crime/with a warrant or is in a whatever suspicious list then they have to investigate more about you and check out if you are the same person they have in the hint.
The problem arise from the memo that appears at the fbi website is that when a name comes with a "hint" the investigation of this hint is apparently almost manually and just imagine ALL the people who are applying and can unfortunately come with a hint.
Good luck,
The FP that the ASC sent to the FBI from your appointment letter, the results come back within 24 hours, that is not the name check.
Thanks!