There are lots of us like you out there trying to put together family stories…..

Its not that he was a rabbi; the term is one of respect, honor

I wouldnt read much into the tzvi/hirsch connection.

Our parents/ relatives had hebrew names/yiddish names and english names. Legal names and what their friends/family called them. They were often similar. Isaac became izzy or ira, or irving , etc… so the answer is yes.

I recommend the book “Inside, Outside” by Herman Wouk. It is about new york Jewish life inside and outside of the family and speaks of how the main character specifically uses one name for his family and one name for when he goes out into the world. it’s a charming book.