That's a Dendrobium. There are a lot of different kinds of Dens that have different climate and light requirements. The kind you have prefers warm temperatures, regular watering, high humidity and fairly bright light throughout the year, but not direct sun all day. Growths (sometimes called canes) normally retain all or most leaves for 2-3 years under good conditions.
Often when moved from excellent greenhouse growing conditions to not so perfect home conditions they drop a few leaves. Underwatering or cold temperatures can also cause leaf drop of this kind of Den.
If you mean it's in the black pot with white pebbles on top, that's only one plant. Many orchids send up new growths from the base of old growths. The growths flower, then eventually send up more growths. You wind up with a number of upright growths together in the pot. This is called sympodial growth. The canes that haven't flowered yet are probably part of the same plant. Some Dens can flower from the same growths for many years.
Some orchids, like Vandas and Phalaenopsis, don't have this kind of growth. They grow continuously upward from the center. This is called monopodial growth.
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