Wendy,

I assume that you are referring to Joseph Kirshman.  As you observed, he appears with that name in all documents in the US, such as the 1930 census.

People were free to be known by whatever name they wanted (except for purposes of fraud).  However, his "official" name change would be part of his naturalization, which can be seen here (petition #94732 , 15 Feb 1928): https://search.ancestry.com/collections/2280/records/3388277

Regards,
David Oseas

Researching:
HYMAN/HEYMAN/HEIMOWITS/CHAJMOVITS: Zemplen-Dobra, Hungary > New York
KLEIN: Satoraljaujhely (Ujhely), Hungary > New York > Los Angeles
KRONOWITH: Hungary > New York
OSEAS/OSIAS/OSIASI/OZIAS: Iasi, Romania > Chicago > Milwaukee > Los Angeles
SCHECHTER/SHEKTER: Kishinev, Bessarabia > New York  
SHERMAN: Iasi, Romania > New York > Los Angeles
STRUL:  Iasi, Romania > Haifa, Israel
WICHMAN: Syczkowo (Bobruisk), Belarus > Milwaukee > Los Angeles