The Doctor’s companion who is a Time Lady from Gallifrey is Romana.
Romana is short for Romanadvoratrelundar, a Gallifreyan Time Lord assigned to assist the Fourth Doctor during the quest for the Key to Time. She first appears in “The Ribos Operation” in 1978 and initially approaches the Doctor as an academically trained equal rather than an inexperienced traveller.
The television series presents two main incarnations of Romana. Mary Tamm played Romana I, while Lalla Ward played Romana II after the role was recast. Like the Doctor, Romana can regenerate, and the differences between her incarnations become part of her character’s story.
Romana is often confused with Susan Foreman because Susan is also from Gallifrey and travels with the Doctor. However, Romana is explicitly established as a Time Lord and is the companion most directly described as a Time Lady. She eventually leaves the Doctor in E-Space alongside K9 in “Warriors’ Gate.”