It's a form of Issac. Although the Polish form of Isaac is Izaak the form Ajzyk is also known. I don't know how much usage it gets now but in the bast it was mainly used by Jews.
Example of usage from Polish language wiki:
http://pl.wikipedia.org/wiki/Ajzyk_Samberg
http://pl.wikipedia.org/wiki/Ajzyk_Rotman