How To Document A (Given) Name Change #names

Martin Kaminer

Hello All,
My maternal grandmother was born Aranka Feigenbaum in Hungary in 1906. She arrived at Ellis Island on August 16th 1927 along with her mother and siblings and is listed as Aranka on the manifest (as well as on the visa application dated 1921). At some point soon thereafter she started using the name, or being known as, Gladys Feigenbaum. She died in 1998 having lived in New York City since her arrival 71 years earlier.
I do not know whether her name was ever legally changed, though her legal documents -- including naturalization -- use the name Gladys, not Aranka. 
How might I determine whether her name was ever legally changed?  If it was never legally changed, what other methods might be used to document this?
Martin Kaminer

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