Myfanwy

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

History
A pteronodon 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 persuaded Jack Harkness to help him catch it. (TW: Fragments) Ianto named it "Myfanwy" after a Welsh goddess with beautiful singing (ironically, the pteronodon's screeches sound horrible).

It became Torchwood 3's mascot and pet, and an essential part of their everyday life, even taking part in a basketball game (TW: Cyberwoman)

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

In TW: Children of Earth: Day One, the entire Torchwood Hub is blown up by the government, possibly killing Myfanwy unless it managed to escape.

Personality
Myfanwy came and went from the main base as it pleased, entering through a large opening on the ceiling. It was well-trained: it returned to the base on hearing a signal from Jack Harkness's wristwatch, and only ate food treated with a certain "barbecue sauce", which Suzie Costello had developed. (WEB: 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 is technically correct, but confusing: "pterodactyl" refers to an order of creatures (order Pterosauria); pteranodons belong to one genus--Pteranodon--within the order. (By way of analogy, Humans belong to the order Primates and the genus Homo.)

Torchwood Declassified mentions that the pteranodon was nicknamed "Myfanwy" by the cast. This is later shown to be the case in-universe, when the Torchwood site featured an IM conversation between Ianto and Owen about Myfanwy's feeding habits (WEB: torchwood.org.uk).