Pudsey

Pudsey Bear was associated with Children in Need.

Eddie Redmayne contacted many people in his search for Pudsey, including the Twelfth Doctor, Tim Peake, Sister Julienne, and Graham Norton, to name just a few. He was eventually found in Redmayne's briefcase. (TV: Looking for Pudsey)

Information from invalid sources
Whilst he was in the Blue Peter studio, he was mistook for a minion by Greg James who then apologised. (WC: Mind My Minions)

He was a temporary companion to the Twelfth Doctor and Clara. He helped defeat Sontarans, Daleks, Colony Sarff and the Mire. (GAME: Doctor Who Game Maker)

Other
Pudsey Bear is the mascot for Children in Need, a charity that Doctor Who has a long association with. The bear was designed by BBC graphic designs artist Joanna Lane in 1985 and was named after the market town where her grandfather had been mayor. Originally designed to just be featured as a logo, the bear soon became much more.

He was added as a companion for one week during Children in Need in Game Maker.

Starting in 2020, merchandise of Pudsey as the Doctor has been commonly released through the Children in Need online store.