One solution for const enums (unnamed enums) is to create a companion array with the stringnames, i.e.
enum { MOVE_GROUNDED, MOVE_JUMPING, MOVE_FALLING }
const state_names := ["MOVE_GROUNDED", "MOVE_JUMPING", "MOVE_FALLING"]
Then to get an enum name you do:
var my_enum_name: String = state_names[MOVE_GROUNDED]
This only works if the orders match, and therefore the index values match.
Probably best to simplify by using a named enum or just a dictionary, since they are interchangeable:
const STATE := {
IDLE = "IDLE",
JUMPING = "JUMPING",
FALLING = "FALLING",
ATTACKING = "ATTACKING",
}
print(STATE.IDLE) # "IDLE"