I'm sorry for the super late response Francine - this inquiry came to me right about the time we moved back to Chicago (11/15/2017) from AZ so it must have gotten lost in the shuffle!
I don't have a true answer to your question - I was told by my Father - Joe - while growing up that when Harry Deinstein was questioned about his name getting on the boat in EU around 1884 that he responded with his Jewish tribal designation "Kohanim" which became Cohn in the messed up translation.
All his siblings remained Deinsteins and the Cohn men (Art, Laurie and Joe changed their names back to the shortened name Dean in the late 30's because they were having a hard time getting jobs with Jewish names. The sisters never had to change their names because they were almost all married/about to be married at that time. Hope this helps!
Sincerely
Mark
madlerdean@gmail.com