Robert, thanks very much for your helpful response. Yes, the family name is in Russian records (from Podolia and Bessarabia) as Schmidt.
It's interesting that an immigrant could "share" a passport ... how did this work? Would someone else in "the old country" obtain a passport and sell it to an emigrant who couldn't get proper documentation himself? Is there any possibility that the fraud could have occurred at the time of naturalization in the 1920s — i.e., Louis Smith no longer had the information on his arrival, so he claimed a false identity?
Since you seem knowledgable about the process, another question: was the name of the "friend" to whom the immigrant was traveling part of the original passport, or did the immigrant just provide that information orally? I'm wondering if the "Dr. Eisig Fischer" listed on the manifest was really my ancestor's uncle, or rather the uncle of whoever might have sold/loaned him the passport.