I guess I never really knew there was such a term, but I suppose it makes sense if you are in the business to circumcise, that would indeed make you a circumciser (which as Dave Barry would say "would make a great name for a band").
In Istanbul, Turkey, it seems that circumcisers have a need to promote themselves in innovative ways. A dude by the name of Ismet Durai (is he even a Doctor??) uses clever tear-off phone number posters. If I was in the need of circumcision services, I'd definitely consider this guy.