When the Sixth Doctor variously referred to the Second Doctor as "I" and "him", Peri Brown told him that she wished he would stop switching personal pronouns. (TV: The Two Doctors)
Alex made sure to get the right personal pronoun as he translated the Sycorax leader's message "surrender or they will die." As it turned out, "they" referred to the population of humans with A-positive blood. (TV: The Christmas Invasion)
Shortly after her regeneration, as she fell through the sky above Sheffield from her TARDIS, the Thirteenth Doctor internally conversed with herself about pronouns. After she erroneously referred to herself as "he", she reminded herself to be careful, as her "personal pronouns are drifting". (PROSE: Things She Thought While Falling) She continued to have trouble with gendered terms during her early travels, as she had recently been a man. (TV: The Ghost Monument)