This is a tricky question - so it warrants a YES and NO answer.
By this I mean that the name check is one third of the background check; the other components are the FBI fingerprint check, and the IBIS name check. Together the three comprise the background check process which is required for all naturalization applicants.
At times, USCIS employees unfamiliar with the process will tell an applicant that he/she their background check is pending without letting them know which component is missing.