Here are the results of my effort to pin down the correct title and attribution of this song.

This impressively thorough Bert Williams discography (in pdf format) says he recorded "Somebody" in 1919. It doesn't mention a songwriter, however.

"Somebody" performed by Bert Williams, is on the Archeophone CD "His Final Releases 1919-1922" (2002). (Mistakenly called "His First Releases 1919-1922" at AMG - All Music Guide.) AMG credits "Hanley" as the songwriter. That would be the composer James F. Hanley.

The Harlem Blues and Jazz Band also performs "Somebody" on "From Past to Present: Featuring and Dedicated to Laurel Watson" (2001).

Under the title "Somebody Else, Not Me," AMG lists 6 recordings, one of which is apparently a different song. Four of them are attributed to "Hanley/MacDonald" as songwriters. That would be the lyricist Ballard MacDonald. Several sources confirm that he and James F. Hanley co-wrote many songs, e.g. "(Back Home Again in) Indiana", "Rose Of Washington Square", "Autumn in New York". The one performed by Dave Van Ronk on the album "Somebody Else, Not Me" is attributed to "Van Ronk/Williams."

Sam Deacon McDaniel also performs "Somebody Else, Not Me" on the Storyville CD "The Jubilee Shows, Vol. 3."

On Van Ronk's live album "Statesboro Blues" the title is given as "Somebody Else But Me" and the only writer credited is Van Ronk himself. I assume this is a publisher's mistake.

By the way, Bert Williams also recorded songs called "Nobody" and "Everybody."