It's a schefflera arboricola. Bright light, let it dryout between waterings. I hope you potted it in well draining soil not some heavy stuff. Be careful of hot afternoon sun...the leaves might get burned with almost white like bleached dry spots.
If its in a window turn it a bit each week otherwise the new growth will lean towards sun.
Its commonly called umbrella tree.
You can search this forum and should be lots of discussions.

It would seem to be a Schefflera, but I'm not the best at ID's....

Josh

HI,
I have one just like it. They don't require a lot of light, mine is in a bright room and gets a little direct sun in the late afternoon, but it's across the room from the window the sun is coming in.

Mine is a slow grower. Getting maybe 4 new leaves per year.

I water it when it's dry approx every 2 weeks. I also use VF-11 with each watering. Mine is in a fast draining soil as suggested.

Good luck,
Maid~

Maid, I bet if you give yours more light it will grow better. They do need much more light than you are giving it. A window across the room is not enough for a scheff.

I just put it in plain old miricle gro potting soil. The other start I haven't potted yet, but it's put out even more growth than the one that is (it has no discernible roots yet, which is why I haven't potted it.) I'm definitely NOT a house plant expert by any stretch, so I appreciate all your help!

Oh no, not just plain old miracle grow. That is so heavy.
It will hold the moisture longer and your plants will rot.
You need to lighten the soil up with some perlite so it will drain. You also don't want a lot of peat in your soil.
Most people don't have much luck with that soil.

Is there something better you would recommend? I haven't found a source for perlite in my area (Salt Lake City, UT), though there are lots of nurseries around, as well as the big box stores.

You should be able to find Perlite at Home Depot, Lowes or OSH.
It will probably be Miracle Grow brand and thats ok. I used to see Schultz but not anymore. It might have a light fertilizer in it so don't fertilize your plant for a while. If you can get it at a nursery with no fertilizer that would be better. A nursery should definately have it especially if they sell houseplants. Don't let them sell you Vermiculite...its not the same.
Not sure about brand names in your area, but any soil that isn't really fine and heavy like MG and also one that doesn't have a lot of peat in it should do. A good bag will tell you the percentages.

Definately don't buy garden or topsoil either.
Whatever you get, most likely mixing with about 25%-40% Perlite should be good.