Looks like a Triangle palm (Dypsis decaryi)- a species that HATES to be indoors or anywhere out of full sun. Do not do well in doors that's for sure. Are very easy to overwater… but can be under watered as well. Just cut off bad leaves… would not worry about peeling off leaf bases as that is likely to injure plant… let them come off on their own. Also plant likes to spread its roots out… you have two in one pot… might be a tad crowded in there.