Welcome Lalarocca. it is commonly known as a Parlour Palm. It's botanical name is Chamaedorea Elegans.
These palms like a cool room and aren't happy if they are allowed to dry out completely. I'm not sure what you mean by down sizing. If you cut the leaves it will ruin them but you can split the individual stems to form new plants. The stems are rather bare at the bottom which suggests that they are old. I did notice in your pictures that you have some new green shoots on a couple of those stems. It may be worth removing one and potting it up to see if it will root and produce a new plant for you.
This is one I had some years ago.
Below you can see a flower spike and if you're lucky they will produce tiny white flowers.