Identification: Please I.D. my Palm Tree

I think this is some kind of Palm tree. Since I started taking care of it approx. 1 1/2 yrs. ago two little trees have started to grow. I water it once a week, it gets lots of sunlight, but the leaves are starting to get yellow. Need basic care instructions, and Id. please thank you

 

Not a palm. It looks like a Dracaena of some sort, but hard to tell with the fuzzy pics.

 

I believe you have a Yucca elephantipes that's suffering from
lack of light. I know you say it's getting plenty of sun but it
really wants to be in FULL SUN all day outside. Now since it's
been indoors this long I wouldn't try giving all day sun in your
yard because it'll sunburn. However you could put it on an east
facing porch or under a shade tree for the Summer to help it
regain some vigor. Only water it when it's gone completely dry.
It's normal for older leaves to yellow and drop off so unless it's
more than 10% or so I'd ignore it. Also check to make sure the
roots are drying out and not sitting in a puddle at the bottom of
the pot which will lead to root rot and yellowing leaves.

HTH
Chris