Myfanwy

Myfanwy is a pteranodon kept by Torchwood 3 as a pet.

History
A pteranodon from an Alternative timeline, where its kind never became extinct, came through the Cardiff rift to 2007. (TW: Everything Changes, Meat)

It was originally found hunting in the countryside, killing sheep at night. (TW: Everything Changes) Eventually, Ianto Jones was able to trap it in a warehouse and to persuade Jack Harkness to help him catch it. (TW: Fragments) Ianto named it "Myfanwy" after a Welsh goddess with beautiful singing (ironically, the pteranodon's screeches sound horrible).

It became Torchwood 3's mascot and pet, and an essential part of their everyday life.

Jack Harkness was later able to use the pteranodon to attack Lisa Hallett, mortally injuring her. (TW: Cyberwoman) The pteranodon, on the other hand, survived the encounter. (TW: Meat)

Personality
Myfanwy came and went from the main base as it pleased, entering through a large opening on the ceiling. It was well trained, being called by a signal from Jack Harkness's wristwatch and only eating food with a certain "barbecue sauce" on it, which Suzie Costello had developed. (torchwood.org.uk, TW: Cyberwoman) The pteranodon also had a fondness for dark chocolate. (TW: Fragments)

Behind the Scenes
The in-universe Torchwood website refers to the creature as a pterodactyl, this caused alot of confusion with Torchwood fans who believed it was a pteranodon, infact, those people had pterodactyl confused with pterodactylus, pterodactyl is a group of creatures, including pteranodon. Torchwood Declassified mentions that the pteranodon was nicknamed Myfanwy by the cast. This is later shown to be the case in-univere, when we read an IM conversation between Ianto and Owen about Myfanwy's feeding habits (torchwood.org.uk).

Technically, it has appeared in every Torchwood episode so far, as a clip of it appears in the series' opening credits.