I have recently created a DNA project for direct patrilineal descendants of anyone with the surname Bürgi. Even if you don't have proof that your Bergey family descends from anyone with that name exactly, if you think it is a possibility, you are encouraged to join!

It is a Y-DNA project, so only men can test; any women wishing to participate will need a male relative who also descends directly on the paternal line from the Bürgis to test. You can test through Ancestry and then join the group; that will add the results to the group automatically. Or, if you test through another company (like Family Tree DNA), it is possible to manually enter your results.

We do have some preliminary results: descendants of Ulrich Bergey, an early Mennonite immigrant to America, match one another and have the haplogroup R1b1b2a1a2c; descendants of John Burcky, a later Mennonite immigrant to America, and descendants of Hugh Parkey, a suspected descendant of earlier Mennonite immigrants to America, match one another and have the haplogroup I2*.

The project is located here: http://groups.ancestry.com/group/burgi