I believe getting RFE on birth certificate or any other doesn't indicate about name-check.
if you are interested in to find about namecheck is cleared or not you may call to Service center and learn, or u may send email to FBI,
Name check is std procedure, ppl are now a days are having miss-Interpretation on namecheck. that trigger panic, they not only have name-check procedure but They also check/gether info like background-check (from consulate your home-country), and here in US if u have any criminal record, local law enforcement record, and even Credit /C-Card/loan issue u have. even trafic tickets and violations (Specialy DUI cases), any civil/crimnal court case pending/close or issue etc. they check all.
You don't need to worry about these std procedures, think in this way, If u are clean u all fine.
Trust on God(whatever ur believes are, and u name him), practice your faith, and pray, everything will be fine

, its just matter of time .
Good Luck