Other than the cuteness of the acronym BIALY, the name should be one
that can be found in a Google or other search on the Web by someone
who is not in the group. The name "Bialystok Interest Association
for Long-Term Yichus" has only the name "Bialystok" that anyone might
think to search. Also, the name should convey to anyone what the
group is about. The word "Yichus" is perfect if you know Yiddish,
but imperfect to many who might be looking for the group, though it
does identify the group as interested particularly in the Jewish
residents of Bialystok.

The best I could come up with was:

Bialystok Interest (or Internet) Association in the Lineage of Yesteryear

Would it help to try to find an acroynym for BIALYS? The S might
allow for a broader possibility for the Y.

Zalman Usiskin
Winnetka, IL, USA