That's actually not a palm, it's a Yucca gigantea. They are pretty easy plants but in low light conditions they can get a little leggy and the weight of their leaves can get too big for them to hold indoors. I think some supports would help along with taking it outside (in complete and all day shade, no sun at all) during the summer. You might want to cut off some of the bottom leaves of each of the trunks to relieve a bit of the weight. If the plant does have another problem going on with it, the good thing is you can always cut it back and it will grow back from the trunk.
You can even cut a big piece of it off and make cuttings from it by putting the cut part of the trunk in water for 2 weeks and then putting some rooting hormone on it and potting it up.

Good luck with it! It looks healthy, just a bit top heavy.
-Alex