Toby is Molly Hooper's cat. She bought him on the 2nd of February. At first she wanted to name him after Sherlock, but she thought he was too "cute and fluffy" so the name didn't fit. Toby is mentioned on Molly's blog - one of the series' Tie-in websites - and the picture of him also comes from there. Her blog is the only place we hear about him, he is never seen or mentioned on screen in Sherlock.
In her blog she explained her intention to buy a cat with this:
"Meena said that every single girl our age needs either a cat or a gay best friend. I figured a cat would be less fuss."
- In Sir Arthur Conan Doyle's "The Sign of the Four," Toby is the name of the dog used to track down a killer.