It's a Syagrus romanzoffiana, Queen Palm. Looks like it might need more water, although the grass looks green enough. The fronds can hang down like that from lack of water but it's also normal for bottom ones to die off as new fronds emerge at the top. Maybe before you moved in the palm went through a very dry period which affected it like that and the fronds were on their way out. Make sure you give it enough water to penetrate deep into the soil. Grass has shallow roots and will soak up all the water near the surface.