It's hard to be 100% certain which one it is, but it is one of the Tradescantia, possibly Tradescantia blossfeldiana variegata or T. fluminensis, common names Inch Plant, spiderwort. These plants generally have trailing stems, and because of that growth habit, they do not sit comfortably on narrow window sills, because they need to trail their growths outside and all around the pot. Yours definitely needs a larger pot, and as it's so desperate, I suggest you do that within the next couple of weeks.
As it looks so untidy, you can cut it back, to a leaf joint - it will regrow. This will also make it much easier to pot on into something a size or two larger, using fresh potting soil. The lengths you remove, if stripped of the lower leaves and made to be about 6-7 inches long including the tuft of leaves at the top, will root if sat in a bottle of water, when they can be potted up after about 4-6 weeks once roots have formed, and you'll then have an extra plant.
All that said, you do need to find a spot for it where it can be allowed to sprawl its growth all around, or something that will allow it to dangle the growth downwards, such as a hanging basket - some images in this link which demonstrate the typical growth habit of these plants http://www.costafarms.com/plants/inch-plant.