It's a Chamaedorea elegans, a small rainforest palm that also does well indoors. They are single trunk palms so you have a bunch of plants there. Don't be surprised if some of the weaker plants die off over time ("survival of the fittest"). They don't like direct sun and need to be kept in soil that stays moist but not soggy. They're very popular because they do so well indoors. If you're seeing some of the fronds deteriorating check to see if it's only some of the smaller weaker plants or just the oldest fronds. Like other leaves, fronds have a limited life and give way to new ones.

Your soil looks VERY DRY, don't be afraid to water palms..., especially those in clay pots. Make sure that when you do water, that the soil gets saturated, your soil looks peaty and those soils can be resistant to moisture once they dry out. Chamaedorea does not like severe drought conditions, they are understory, rainforest plants.