Cross-dressing

Cross-dressing was the act of wearing items of clothing culturally associated with another gender, for disguise, expression, or convenience.

Rose Tyler, a human from 2000s London, was scandalised to find that a Slitheen impersonating the Ninth Doctor was a girl, Slist Fayflut Marteveerthon Slitheen. Though Slist saw nothing of it, Rose made a point to note that she was a "cross-dressing Slitheen" for wearing a synthetic skin suit of the male Doctor. Rose quipped that Jack Harkness would "love [her]" for that. (COMIC: Doctormania)

Similarly, the matriarch of the clan Klep-Clotch Slitheen wore a suit made from the skin of Sir Edward Scott Cameron. (AUDIO: Death on the Mile)

The Second Doctor disguised himself as an old woman while hiding from the British in 18th century Scotland. (TV: The Highlanders)

The Third Doctor disguised himself as a cleaning lady while infiltrating Global Chemicals. (TV: The Green Death)

Several incarnations later, the Thirteenth Doctor noted that she hadn't shopped for women's clothing in a while. After regenerating from her male predecessor, she remained in his clothes for an extended period of time before acquiring an outfit of her own from a charity shop. (TV: The Woman Who Fell to Earth)

While living with Panda in the 2000s, Tom once dressed up in drag for Halloween, and called himself "Eartha Wydenfire". (PROSE: The Golden Hendecahedron)

Behind the scenes
Tenth Doctor actor David Tennant cross-dressed as he played the role of a female companion to the Doctor, played by, in a comedic sketch as part of an episode of Channel 4's.

Every actor in the role of the Doctor except for William Hartnell and Paul McGann has cross-dressed as part of a role in a TV show or film, while Patrick Troughton, Jon Pertwee, and Jodie Whittaker have done so on Doctor Who itself.