That is a Sansevieria trifasciata. Could look a lot worst and there is hope. A couple things I would personally change......but first a couple questions. Where are you in the country? How warm is that room over the winter? It looks like it is not right next to the window but still getting some direct sun which is good. Now you really don't want it planted deeper than it was growing before as you will rot the base of he leaves. Maybe 0.5 centimeter deeper might be ok but really you want it the same. Stake it if you need some extra support while while it grows new roots and rhizomes. The warmer the temperature (and the more actively growing the plants is) the more moisture they seem to tolerate. Sans do like good aeration and drainage at the roots. However S. trifasciatas seem to like a little more moisture than some of the thick-leaved Sans. Once again if it is cool and dark they need to be on the dryer side or they could rot (even moreso with the variegated versions). However, if it is warmer, and they are getting light, they will grow and need a little more moisture. Many folks on this forum swear by Al's Gritty Mix and I am sure they do very well with it. Personally I prefer some real soil around the roots. My personal mixture is about almost 1/3 cactus soil, 1/3 perlite, and some coarse sand and good compost mixed in. This is well aerated but still holds onto a little moisture and some nutrients. Al's mix will need to be lightly fertilized more often, but even if you keep it I would not fertilize much or at all until growth begins. Generally these plants are more actively growing (and need more fertilizer) during the warmer late Spring through early fall. I don't fertilize in winter or late fall and minimally in very early Spring.

The lighting looks good.....in that it is bright and still being hit with some somewhat direct sun (as evidence by your first photo). I can't tell how much deeper you planted it, but it is generally not good to bury plants deeper than they were growing.......but a little might be ok. In a loose mix like the gritty mix it will be more forgiving than in a heavier soil of a LITTLE deeper. Keep it on the drier side over the winter....it probably won't do much at this time. If the leaves begin to shrivel/wrinkle it might need a little more water. Water it with warm water on the morning of a sunny day (e.g. you don't want cool water sitting on it over night.......better to water earlier in the day so any excess can drain or evaporate) Days are short and temps are relatively cool. As the days get longer/warmer/brighter next Spring start watering more often and later (after new roots are well established and the plant is actively growing) you can begin regular fertilizing. If you have a protected outside spot get it outside for a couple months in the summer after the weather warms up (e.g. June to August). This usually helps them put out a bunch of new growth. Probably will get a bunch of nice sturdy new pups by the time you bring it back in again in late summer.