Looks to me like a Fishtail palm.

It looks a lot like a foxtail palm to me. Fishtail and foxtail palms look very similar when they are young because of at that age the leaflets look pretty similar, but your pic looks almost exactly like my young foxtail palms.

A pic of the fronds would definitely help too though.

-Alex

I'd think Foxtail as well. They have that specklyness on the petioles. Also the leaflets on the fishtails tend to be broader.

It look almost as if all the palms have been torn. I really like it and want to take the right steps to keep it healthy.

The branches weap

It is definitely a foxtail palm. The torn look is perfectly normal, that is how the fronds look on this species. It adds to the really full look of canopies on mature foxtail palms.
They are not great palms for indoor growing year round so I do recommend you take it outside in the shade during the warmer months (you can always take it in if you're expecting company, and it will probably have to stay indoors during the winter if you live in a cold climate). During the winter it will definitely help to take it outside to get some water or rain during warm spells if you have any in your climate. They do not like to dry out so make sure that the soil is moist but not waterlogged whether it's indoors or out.

Good luck!
-Alex

They're very easy to grow, but a lot depends on your climate. Normally they prefer strong full sun but you can't have it in shade then move straight out into the sun. It needs to adjust slowly to a change like that.

I live in MN so I'm in a cold state. I'm worried about pest when I bring it outside that might damage it.

much more likely to get pests indoors than outdoors... spider mites and even mealy bugs are problematic indoor pests.. outdoors spider mites are pretty rare. Mealy bugs are rare if no ant infestation. Not sure what other pests you would be concerned about in Minnesota... plus being outdoors is WAY better for the proper growth (at least while it's still warm out).