Fingerprints clearance has nothing to do with the name check. Almost everyone who is stuck in the name check has an EAD, which means that their fingerprints have cleared. That basically ensures that these people are not wanted for a criminal charge or anything of the sorts.
The name check is initiated as part of the background checks USCIS performs on every applicant before giving them immigration benefits. Those background checks also include the Fingerprint check.
The name check consists of running one's name against all records in the National Name Check Program (NNCP) database. The name is altered in various ways to account for the variations in spelling and pronunciation. The DOB is also used. If your name matches the name of someone who has a record at the FBI (be it a witness, an accomplice, a terrorist...), then the system identifies you as a 'Hit'. An officer will now manually compare your file against the files of those whose names you matched. This could be tedious for various reasons, mainly that not all files are stored in the same locations, that is the files might have to be ordered from locations all across the country, and that the department is seriously understaffed. The process is very random, IMO, and doesn't make much sense, since there's a lot more to a person than a name and a DOB.
Hope that helps. Google name check, and read the congressional testimonies of FBI directors to get a better understanding, and go the Citizenship forum on this website, it has some very useful information on the process and how to fight it.