Well, that depends on which specific version or adaptation of 'A Christmas Story' you're referring to. Different renditions might give the little boy different names. You might have to look into the details of the particular one you have in mind.
In the Christmas story, the main character who is a bundled up boy is Ralphie. He has this big adventure where he really wants a Red Ryder BB gun for Christmas. He goes through all kinds of situations, from dealing with his family to facing the big, mean Santa at the store. And all through it, we see him bundled up in his winter clothes because it's cold during Christmas time in his town.