I'm afraid a positive ID isn't possible. There are thousands of cymbidium hybrids. But that doesn't make the plant any less desireable, in my opinion. You should definitely repot as soon as you cut the flower spike. You could divide, but I see a new growth going as well, so I would hold off and just up the pot size. Make sure the new pot is big enough to accomodate that new growth becoming a bulb without squishing it, and has room for something besides roots.
People say they like being crowded, but they need some room to grow!