After you split a plant, it will not flower the next cycle...sometimes for a couple flowering cycles. Don't quote me; but that looks like a cymbidium. Unless you own a greenhouse; you won't usually be able to get these to bloom until you have it pot-bound with maybe 3 or 4 growths. Before splitting most orchids, it's best to look up what kind it is and go by the repotting instructions. I used to over-split mine and now realize sometimes it's better to leave extra p-bulbs on a plant. They stay healthier and bloom better and more often. The plant looks great, you may get lucky and get flowers next spring....If you have any pictures of the flowers it will be alot easier to id this one.