I suppose it may be cheating to nominate a minor-league player, but the first one that came to mind for me was "Bourquise" from T209-1. I don't think anyone knows who he actually was. His name doesn't appear in any database of minor-league players, and I don't think he's appeared on any known roster, etc. The card lists his team as Rocky Mount, but he's wearing a Fulton jersey. Further, of the two Fulton-based teams from that era, neither were active in 1909 when the set was released.
To summarize from T209-contentnea.com, "The issuers of T209 managed to include - as one of only sixteen - an unknown player from a nonexistent team!"
Doesn't get much more obscure than that. Plus, it's his only card ever, and T209-1 is a borderline rare set, with only about two dozen graded cards of each player between PSA and SGC.
