K9 (A Rose by Any Other Name)

A model of K9 lived with the Tenth Doctor in the TARDIS. K9 joined the TARDIS team while Rose Tyler was still on-board, but the robot would initially spend most of his time within the TARDIS, rarely mentioned or seen. K9 only began to actively join adventures after the Doctor adopted a cat, whom he named after Rose. The two did not get along.

Biography
K9 travelled with the Doctor during his adventures with Rose Tyler. Rose and the Doctor once considered purchasing a cat, but decided that K9 was enough for the team. (COMIC: Untitled)

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)

Behind the scenes
Considering that the K9 the Tenth Doctor gave Sarah Jane Smith in School Reunion was named K9 Mark IV, and this K9 was first mentioned traveling with Rose Tyler shortly after this, that would make this version K9 Mark V.

K9 (A Rose by Any Other Name)