It does appear to be a Coleus 'Abbey Road.' Most folks grow these as annuals outdoors and discard them when cold weather arrives. Cuttings in water will survive quite easily over the winter. However, Coleus can also be grown indoors year round. I have one that is now in its third year and has never been outside.
Indoors it has to be in a very sunny window and the soil kept moderately moist. A frosted window will not provide enough light. It does not have a dormant period, although growth does slow down as the day length shortens. To keep it looking presentable through the winter months, you have to keep it pinched and pruned back substantially, especially as spring arrives. That is the only way to keep it from becoming leggy.
Do NOT repot it at this time. As the light reduces so will the growth rate of the plant and its roots. If it is truly potbound next spring, that would be the appropriate time to repot, although mine has been in the same pot for three years and is doing just fine.
