There is no such thing as a , "name check." There is a background check. Your fingerprints will confirm your identity and whether you have a criminal record.
What ever you are planning you may want to consult with an experienced immigration attorney first.
The USCIS may use a background check is any new adverse information has entered the file. If you think you may have such situation it is advisable to work with a good immigration counsel to present the issue well.
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