Looks like a Dracaena (not a palm or ficus)- related to Agaves. These need minimal fertilization, as do most indoor plants.

Definitely looks like a yucca guatemalensis that is growing in very low light. They are very easy to care for. I would bring it outside during the summer in a spot that doesnt get too much direct sunlight (they can handle full sun but yours has been growing in an indoor environment for so long that it won't be used to a lot of high light). They dont really need much fertilizer and definitely thrive on neglect. I bring mine outside during the summer and back in during the winter and they are growing happy. I always let it dry out a little bit between waterings but not too much.

The leaves will grow longer in shade (like the way your's are now) and will only be half that length in full sun.

Good luck with it!
-Alex