He claimed birth in Port of Spain, Trinidad, 1895, and Brooklyn NY in 1902, and that his family moved to Trinidad when he was two years old. The name on his passport is Edgar Leon Sinclair (New Yorker article by Joseph Mitchell). He also used the names St. Clair and Hendricks. He died in New York in 1977, where he spent most of his life.
He worked steamships and may have made different claims to satisfy employers, I don't know.
Houdini was first used in 1916, when he was with the "African Millionaires" group.
Most of the above from www.allmusic.com/artist/wilmoth-houdini-p39437/biography