Why is it called 'Cherry'?

Because that's what Beth called him early on in the movie, in reference to being a virgin.

Beth calls him 'Cherry' because he's still a virgin.
The theme of virginity is heavily present in the film, also, trying new stuff, 'popping the cherry' is the general moral.

Risking being redundant, cherry is a euphemism for virginity.

The virginity thing, the fact that cherry is also used as an euphemism for anything that is pristine, precious, untouched, brand new, mint, unused, etc. Which given the main characters sheltered life up until that point applies as well.

We also have the symbology of the cherry stem that bookends the movie.