What is the name of the professor who shelters the Pevensie children?

The professor who shelters the Pevensie children is Digory Kirke.

In The Lion, the Witch and the Wardrobe, Peter, Susan, Edmund, and Lucy are evacuated from wartime London to the country home of Professor Kirke. There, Lucy discovers that an old wardrobe provides a passage into Narnia. Kirke is initially offstage during the children's first adventure, but his unusual house and open-minded response to their story are central to the plot.

Kirke is also the boy Digory in The Magician's Nephew, which was published later but explains the wardrobe's origins. As a child, Digory helps witness the creation of Narnia and brings back an apple whose tree eventually provides the wood for the wardrobe. This makes the professor more than a host: he is connected to Narnia from its beginning.

A common mix-up is calling him simply “Professor Kirke.” That is a natural shortened form, but Digory Kirke is the character's full name. He later appears among the Friends of Narnia in The Last Battle.