Peter, the comic relief/jester for the play

I don’t know the editorial answer for why this name sometimes appears, but I think you can avoid the problem because this is simply a very, very minor character. I would also avoid singling him out with this kind of label.

The letter scene is indeed comedic (we talk about literacy/illiteracy, book/writing imagery, and control of information) and the servant is a bumbling Shakespearean comedic type, but I wouldn’t describe him either as a true clown figure or as the primary comedic relief. A Shakespearean clown is often more wry and insightful, but the humor in the letter exchange derives dramatic irony rather than sardonic wit. And a good deal more comedic relief comes through Mercutio and the Nurse, say, than this figure.

I think it’s a subtle mislabeling that lends the servant too much thematic weight, and without that, it’s probably fine to just refer to him as the illiterate messenger and move on.

It can be fun to play “what is the deal with this tertiary character?”, but if these kids are reading Shakespeare for the first time, I don’t think there is much benefit to spending a long time on that scene in particular.