Hi,
welcome to the forum.
It is either an elm or a zelkova. As I have neither, and have never looked into the species, I;ll leave it to others to properly identify it.
One thing I can say.. THis plant is currently very unhappy. Do you know where they got the plant? It will need a bit of TLC for it to survive till spring.
Make sure it is not sitting on top of a radaitor. Give it plenty of light. Water when the soilsurface is starting to dry up (Too wet is nog good) and do not let it dry out (Completely dry = dead plant).
At this stage I would consider taking the plant out of the current container, and potting it up in a somewhat larger pot, using good quality potting substrate. That will aid in recovery.