why use the same kid?

[deleted]

Yes it was the same kid.

I can see two explanations for this, both of which could be right.

The same kid could have been used to reinforce the idea of the repeating cycle of life. Ends become beginnings, effects become causes, the year progresses until winter turns back into spring to start the whole thing over again. The "seasons", both of the natural world and of a human life, are obviously one of the important motifs of the movie. There's also sort of a tie-in with the Buddhist idea of karma.

I also thought the kid was shown for psychological reasons. Maybe it was only the same kid in the monk's mind, since the young boy reminded him of himself at the beginning of the movie. Of how much he had learned through the course of his life, and what he might be able to teach the boy, as his master taught him.