I don't think that is a banana plant,but I do think that variety will grow in clumps no matter what you do.It certainly needs a bigger pot.I want to say that is called a bird of paridise but I'm not sure thats correct,it's a fairly common tropical plant so I'm sure someone on here will know.

White Bird of Paradise -- Strelitzia Nicolai. Look it up. It's an easy-to-grow 'house plant'. Home Depot sells a ton of them. Indoors they get huge because the leaves and petioles stretch in lower light levels and in a few years it will outgrow your room. Outdoors they remain more compact. Don't expect any blooms unless you grow them in a conservatory.

Strelitzia nicolai is one of my favorite big tropicals. It is a cousin of bananas (Musa), thus the similarity of appearance. I like nicolai much better than the much more dwarf S. reginae (orange bird). These want to become BIG plants with enormous leaves and petioles regardless of whether you grow them inside or outside (conditions permitting). Your plant seems very healthy. You can divide them if you want, but I would leave them together (they naturally are clumping and will constantly from side shoots anyway. If you do put it outside, select a site with some shading from direct sun as it probably hasn't seen too much direct sun recently. Alternatively, just get it used to its interior site (it's kind of late in the growing season anyway). I would transplant the plant (the white pot in the photo is about right in size). Use a well-drained soil and let the soil dry somewhat between watering--especially in the Winter.

I recognised it as a BoP as I have a S. Reginae flower, but how do you tell from the pic that it's a White and not the Orange one...just by it's size?? If so, why couldn't it be a Reginae that has been grown in less light? Just curious.