Don’t forget that Jewish children from the 19th century onwards had gentile names for civilian authorities and Jewish names for internal Jewish communal use and for boys especially a necessary name needed to be called for a Thora blessing.
Jewish immigrants from Eastern Europe who did not have specific gentile names start to use them when immigrating to the US. Examples who are not always the same: Mordechai can become Max, Gittel can become Gussie, Rivka can become Rebecca, Rose, Schmiel became Sam and the classical Sean Ferguson was originating from Russia with a family name something like Forgatson (don’t catch me if this name is a little bit different), but the ‘Shoyn fergessen’ – (I forgot) was a classical Jewish joke in the 1930s.
On the other hand it often happens that people had two different first names and we see this in the files of JRI-Poland where once a mother is called Malka, a second time Channa and another time Channa Malka. And all 3 versions of those first names were used. So I won’t wonder if that person would use the name Annie for Channa and Regina for Malka for different purposes in the US.
