What’s in a name #names
At www.familysearch.org the surname BUNIM gets 505 hits.
Database did not allow searching as first name only.
On The Ellis Island Database https://stevemorse.org/ellis2/ellisgold.html
the first name BUNIM gets 15 hits. No hits for BUNIM as surname. But, there are variations of Bunimowicz.
It was common in Galica for couples to marry religiously, but not civilly, and civil birth records often listed the child under the mother's surname rather that the father's.
Patronymic can refer to a surname created from a male ancestor's first name by adding a suffix.
Hope this helps,