The Dancing Doctor was a nickname that Doctor Beverly Crusher had been given due to her having won several awards in St. Louis for tap and jazz dance, prior to her posting aboard the USS Enterprise-D. Wesley Crusher was aware of his mother's monicker. (TNG: "Data's Day", "The Game")
In 2367, she was reluctant to offer lessons to Data for fear that she would reacquire this nickname. (TNG: "Data's Day")