it is "name check", nothing with Finger print (typically FP result will send back to USCIS within 1-2 days since all handled by computer).
For name check, if there is some hits with you (no one really know what trigger the hit, see articles here), then it will require human involved and which cause the delay (some unluck one pending for a few years).
Since the "name check memo" not applicable to naturalization, you can try to contact with senator/congressman/USCIS/infopass (keep all receipt). and still no result after over 1.5-2 yrs, then WOM is the good option. see details for WOM 這裏
For name check, if there is some hits with you (no one really know what trigger the hit, see articles here), then it will require human involved and which cause the delay (some unluck one pending for a few years).
Since the "name check memo" not applicable to naturalization, you can try to contact with senator/congressman/USCIS/infopass (keep all receipt). and still no result after over 1.5-2 yrs, then WOM is the good option. see details for WOM 這裏