Hi! I am new to this website. I searched and searched but I couldn't find anything on what kind of palm this is. Does anybody know?

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I am known for the greenery around my desk, and was asked to save it by a co-worker. It used to be in the stairwell, with an open connection to the ground lobby, and was tall and luscious. It was somewhat near the door, and there isn't forced air in that area. It was then moved to some one's private office - much less light, forced air, and much smaller space. Now, one of the three crowns has broken off completely, the other two are in poor shape. Its been in the same pot with plain potting soil and only watered with plain water (I think) for probably at least six years. We live in Olympia, WA, which is very cloudy! But our building gets LOTS of light. My area gets lots of direct light in the am, and indirect all day. There is a back stairwell I could put it in, that gets very hot, as there is lots of direct light all day and no air circulation.

Should I cut the stalk further down - will it sprout out from the edges of the cut? What about the odd loss of leaves from the ends of the two other stalks, but how its kept leaves further down?

I'm stumped! Any and all advice muchly welcomed and thank you in advance!

Yuri