Rose-the-cat

Rose-the-Cat was a cat the Tenth Doctor adopted after Rose Tyler was trapped in Pete's World. He decided that Rose was the perfect name for the cat. Rose, K9, and the Doctor lived together without any other long term companions.

Rose would often try to help the Doctor cope with the loss of his former love, through various means. Most to all of these failed. Despite this, her time on the TARDIS did note a sharp contrast in the performance and character of the Doctor. While he would initially avoid leaving the TARDIS or having adventures at all, by the time she left he was not only actively seeking out trips once again; but he also eventually decided it was time for him to take-one another companion.

Rose eventually left the TARDIS team, searching the cosmos for a new person to comfort as the Doctor decided it was time to find a new companion. After an immeasurable amount of time in stasis, Rose emerged to find the real Rose Tyler standing in front of her pod in a state of confusion.

Biography
The Doctor adopted Rose during a fit of depression, and named her after his now-lost companion Rose Tyler.

Owning a cat was initially far from what the Doctor expected it to be. Directly after bringing her into the TARDIS, Rose scratched the Doctor up and ran off. The Doctor would not see her for five days. When he did see her again, he lectured her for being "a bit rubbish," but Rose mainly ignored him during the conversation.

The Doctor at one point spent an entire day sulking in bed and crying over the loss of Tyler. Attempting to cheer the Doctor up, Rose-the-Cat managed to pilot the TARDIS to various locations in space-and-time to track down animals to hunt. She then presented their carcasses as gifts to the Doctor, which only made him more sad over the death of all of the various creatures.

The Doctor in another instance entered his closet to discover that Rose-the-Cat had pulled down all of his suits and sat on them, leaving them covered in neon hair. The Doctor planned to travel to Deva Loka to relax, but discovered that Rose had scratched up his long brown coat, ruining it. Enraged, the Doctor left Rose dangling outside in a space-suit as he considered how he was nowhere near as merciful as he used to be.

Rose warmed up to the Doctor's presence and after a while the two began to get along fine. Rose at one point asked the Doctor if he had ever had any other pets in the TARDIS, to which the Doctor admitted that there was someone that Rose needed to meet. That "someone" was a personal version of K9 which the Doctor kept on the ship. Standard for most dogs and cats, the pair did not get along. Their first encounter ended with Rose attacking K9 with the Sonic Screwdriver and K9 entering "defense mode." The Doctor once again resulted to leaving the two dangling outside the ship as punishment. (COMIC: A Rose by Any Other Name)

Personality
Rose-the-Cat was, by no one's standards, human. Rose would often have trouble understanding the Doctor; partially because of his insistence on never moving on from his past, but also mainly because of basic misunderstandings which fell from her being a cat and him being a Time Lord.

Rose would often only think of herself. While she often encouraged the Doctor to move on and find a new companion, it was more often than not because she found his constant ranting and bickering to be annoying. She was easily bored and easily annoyed, and she would never try to hide how she felt.

Rose showed a surprising lack of concern for the effects of time travel, and she would often cross her own timeline simply to avoid mildly annoying circumstances or events. She at one point sent a shockwave of paradoxes across all of time-and-space in an attempt to create a cat flap in the TARDIS' wall. (COMIC: A Rose by Any Other Name)