K9 (A Rose by Any Other Name)

A model of K9 lived with the Tenth Doctor in the TARDIS, and began to actively join adventures after the Doctor adopted a cat, whom he named after Rose. The two did not get along.

Biography
After the departure of Rose from the team, the Doctor would indeed adopt a cat, just as Rose had suggested. K9 and Rose did not get along, and fought within the TARDIS on several occasions. (COMIC: A Rose by Any Other Name)

K9 (A Rose by Any Other Name)