This dubious passage from The Secret Life Of Houdini by William Kalush and Larry Sloman tells of Harry's family arriving in New York in 1878. The family's name in Hungary was "Weisz."
They arrived in New York on July 3 and were processed at the Castle Garden immigration building, where each of them received a new name. Since Cecilia didn't speak English, her responses to the officials were in German. So their names became English variants of German names. Armin became Herman, eight-year-old Natan just had an "h" added, six-year-old Gottfried Vilmos was dubbed William, Erik turned into Ehrich, and Ferencz Dezso was officially named Theo -- later to be nicknamed Dash -- and the family name became Weiss. [Link]Ehrich must have made a return trip to Castle Garden to have his name changed to "Harry Houdini." Here's a good explanation of why stories like these are bogus.