It depends on the nature of variation. Is it only a spelling mistake and in case so, up to what extent the variation exists or it is absence or presence of surname or presence of a totally a different name. The full name as printed on both the documents should be given by the author to enable any meaningful advice in the subject matter. In case of only a spelling mistake of minor nature, it may not pose much problem. Sometimes submitting an notarized affidavit works. It also depend on the attitude of the official who actually verifies the documents.