I know if there were hundreds they wouldn't be able to give you an answer but what if there were two possibilities, would they get in touch to see if they could get you the right one or would they just come back again saying couldn't find it?
I don't think they would contact you, however I believe you can add extra details ie. say that you don't want it unless the father's name is John.
I always use Freebmd first to get as many details as possible so that I can quote the district, volume and page number. That way you are far likely to get a certificate as they can find it easier. Without that they have to search and there is the possibility of it being missed.
