[Facts] Additional to that . . .
in reply to a message by Miranda
. . . The most likely source of Fanny in your relative's case would be a Latvian or Yiddish version of Frances, or a Latvian or Yiddish name which resembles Fanny or Frances. I had a quick look and the only obvious condender was Freyde (click hyperlink for details), however I have no idea whether this was ever popular in Latvia - information on Latvian names is elusive unless you speak Latvian!
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My Grandmother was Jewish and from Latvia. Here sister, who always lived in Latvia, was named Fanny. I never heard another version of her name. Seems that it was used in Latvia at the time (1920s). Other female Jewish relatives in the US during the same time period (e.g. a sister of my other grandmother) were also named Fanny (and I never heard a variant either).