the tag in the pot looks like one from Matsui Nursery. They do wholesale of unnamed hybrids, and will not say what the cross is.
many cymbidiums like to be root-bound, so when you re-pot, you should look for something about 2 inches larger than the one it's in (6 inches should go up to 8 inches, if possible). I don't reccomend going up to 1 gallon until it's out-growing a 10 inch pot