If the NBA goes through with its plan to have Heat and Nets players wear nicknames on their jerseys, it will be unusual -- but not unprecedented.
Several NBA and ABA players, including such stars as Pete Maravich and Elvin Hayes, wore nicknames on their backs in the 1970s. You can see some examples here. Nicknames have also appeared in college hoops, as you can see in this 1971 shot of Maryland guard Howard White.
Nicknames on the gridiron are rarer but not unheard of. In the AFL, Edward "Wahoo" McDaniel wore his nickname. So did Joe "Turkey" Jones in the NFL. And probably the most notorious player nickname of all was worn by Rod Smart of the XFL's Las Vegas Outlaws, who famously wore "He Hate Me." (Smart later played in the NFL for the Carolina Panthers but wore just his surname.)
One other item of note: Adam "Pacman" Jones has never worn his nickname, but he did manage to wear his nickname's first initial when he was with the Titans.