In the Bialystok area, there are many people with surname of Bialostocki (and similar spellings). I would assume that the surname Bialy is a shortening of the Bialostocki surname. 

As for Bialy's. They are definitely not bagels. They were a staple of my and your Bialystok ancestors lives. As Glenda says, the full name of these "rolls" was Bialystoker Kuchen. In the US these days Bialys are sold in many places, but the only ones that look and taste like the originals are at Kossar's Bialys in New York's Lower East Side and other bakeries in New York City. For more about this Bialystok delicacy, read Mimi Sheraton's book "The Bialy Eaters."

BTW, there is one restaurant in Bialystok that sells Bialy's, but they are small rolls with some poppy seeds on top -- tasty, but definitely no comparison to real Bialys. 

Mark Halpern
son of a Bialystoker mother