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Looks like a Pygmy Date Palm (Phoenix roebelenii) to me. The leaves off the frond are relatively flat, and they are narrow and widely spaced. But the sharp spikes on the frond near the trunk are the biggest clue.
I don't think it's Areca Palm (Dypsis lutescens, golden cane palm). Areca has more of a V shape to the leaves off the trunk. And the leaves are wider and closer together. Multiple trunks, even when quite young. Plus, no spikes.
I don't think it's Bamboo Palm (Chamaedorea seifrizii). The leaves off the fronds are flat, but wider. Multiple trunks, even when quite young. No spikes.