In this question various surnames are explored that are strongly associated with being a Kohein. Some of them are rather unambiguously chosen simply because the chooser wanted to indicate their status. Others are more coincidental in nature (e.g. Rappaport), and some are contra-indicators (e.g. Hadad).
For a name that pretty strongly indicates Kohen lineage, if a Kohen is suggested a shidduch with a woman who has such a maiden last name (eg "Katz," "Cohen" or maybe especially "Hadad") but whose family has no claim of being Kohanim or any knowledge of how the family came to possess that name, should he be concerned that the family was in fact a family of Kohanim and then became Chalalim, or should he just regard the name as a coincidence?