One of my relatives born in Poland in 1886 was listed as "Gołda Lustgarten false Turner".   Does that mean that her last name should have been Turner and not Lustgarten?   

George Frankel
Researching:  Turner/Lustgarten  Krakow, Mszana Dolna, Kalwaria, Oswiecim, Wadowice, Nowy Targ, Nowy Sacz, Poland  

Dear Mr. Frankel,
I can think of two options: It can mean, that in another document she was mentioned as Golda Turner, what was wrong since her name was Golda Lustgarten. Or - it is a reading mistake and instead of "false" it should be an abbreviation of the German word "vormals", "formerly".
A good and healthy new year
Wolfgang Fritzsche, genealogist, Germany

But listed where?
-Ari Dale

Emily Garber has an excellent presentation that covers this. The name following false or (f.) is one that the person was using but was not the legal name. So Golda Lustgarden was her correct legal name, but she went by Golda Turner. This could have been because her parent's marriage was not officially recognized (married only in the religious sense but not civil, for various reasons). Or she could have just started using Turner to sound less Jewish, as another example. There was an opportunity on Naturalization papers to change a legal name at that time, but only for some time periods.

--
Jeff Goldner
Researching Goldner, Singer, Neuman, Braun, Schwartz, Gluck, Reichfeld (Hungary/Slovakia); Adler, Roth, Ader (Galicia); Soltz/Shultz/Zuckerman/Zicherman (Vitebsk, maybe Lithuania)

Exciting what was said above, here’sa personal example:

My great-grandfather was Josef Bermann false
Lehrhaupt. His father was Perez Lehrhaupt and mother was Sara Bermann. They were only religiously married and not civilly. Consequentially, the children carried both names. 

Moshe Berman,
Boca Raton, Florida 

Researching: Berman, Lehrhaupt, Gelb, Gold, Rabinowitz, Schroit, Wejc, Meryash, Tropper, Gonter, Tesler, Melamed, Jaeckel, Perlstein, Hillowitz