Without wasting any more time, I am going to skip ahead four volumes and reveal that the narrator's name is Marcel, or just M.
I don't know why Proust makes us wait until Volume VI, The Fugitive, to learn the narrator's name, but he mentions it only once, and very briefly. You'll miss it if you are not alert.
Right now we are in the middle of Volume II, Within a Budding Grove, and M. is not a boy anymore — he's around 16 when he leaves Paris with his grandmother to spend the summer at a seaside resort called Balbec.
For expediency, I think it's time I refer to him as M. and get on with it.