This sometimes appears as Hanzerburg in the PRDH database.
I have a theory about this. In the book Oxford Dictionary of Canadian Place Names by Alan Rayburn, on page 160 there is some interesting information about the Newfoundland town of Harbour Breton. In the 1600's, it was known to the French as Havre Breton, and sometimes as Havre Bertrand.
I try to imagine the Englishman John Dicker pronouncing this name to French priests some years after his capture.
A Frenchman would say "AUV-ruh bruh-TONE" or "AUV-ruh bare-TRAHN". But an Englishman like John Dicker might say "HAV-ver BERT-rand" or "HAW-ver BERT-rand", pronouncing it with English phonics and emphasis on the BERT.
In this case "HAV-ver BERT-rand" sounds quite a lot like Hanzerburg, and "HAW-ver BERT-rand" sounds something like Hauserburg.
To a French priest who knows no English, this may have resulted in the Hauserburg on these certificates.
I checked for Oserburg, too -- there's one in Pennsylvania, but that's a little far off for John Dicker...