In 1903, immigrants often had no papers, and the passenger lists were made
up by the shipping company with the names on the tickets. My cousin came
to the US in the 19teens-under another name which I know.
It seems that the fiance of a girl in her home town bought a ticket to
bring his future wife to the US. But the girl died before the ticket came
or the ship sailed. The family sold the ticket to my cousin's family-so it
wouldn't go to waste. My cousin then came to the US under the name of the
dead girl-and used her right name once she was here.
Bottom line is that there were often no papers. There was no need to go to
court and change a name-you used whatever name you wanted and unless you
tried to defraud someone that was fine.
So Dora whatever became Dora Goldstone so that she could pass as a sister.
Then if she wanted she could revert to whatever her name was-or change to
something else entirely.