Which sports person is nick named Denis the Menace in tennis?

Answer 1

Former US player, Dennis Ralston
... though, for a minute, I thought you got the sports mixed up:
I initially thought of Denis Towers, Australia, who was undefeated champion doubles wall handball player in Victoria Australia, and won 3 state singles titles in a row in the 1980's, was also undefeated in the very popular, 'end-to-end Australian football' during the 60s and 70s and later invented the team game of Grappleball, in 1999.

Answer 2

Dennis Keith Rodman