Can you please name this plant? And tell me how to best care for it? Thanks.
The plant in the photographs you have sent is a definitely a kind of begonia. If I had to guess more specifically than that, I might guess that it is a certain cultivar called a ‘Corallina de Lucerna’. There are thousands of different kinds of begonias out there and each one will have one of three different kinds of root systems: fibrous, rhizomatous, or tuberous. Begonia ‘Corallina de Lucerna’ has a fibrous root system, consisting of many fine roots that tangle instead of roots consisting of larger fleshy rhizomes or tubers. Based on that assumption, this is what you need to know about caring for your plant.
Your begonia requires bright light but does not need direct sun. If you wanted to try and get it to flower you would have to increase the sun to the point where the plant is getting about 4 hours of direct sun a day. However, where you have the plant now, if it is under florescent light on a daily basis it should be getting enough full spectrum light to be able to properly photosynthesize. During the summer months you can keep the soil moist on a regular basis, or allow it to go slightly dry between watering, but in the winter you want to water less. The plant is much less active this time of year so you can let the soil go fairly dry between watering. You will want to give it a weak solution of a balanced fertilizer every two weeks during the summer months only, when the plant is getting more sunlight and growing at a faster rate. The only other thing is that begonias love humidity. If you placed a layer of small stones or pebbles in the saucer underneath the pot and let excess water accumulate there, then the water in that “buffer zone” can evaporate and provide some humidity for the plant. As long as the roots are not sitting in water for any length of time, which runs the risk of root rot, the begonia will benefit from the extra moisture in the air. Since our places can get so dry in the winter I might even put a little water solely in my saucers if the plant’s soil is still moist and does not appear to need more water. As far as the container it is in, it should be fine. You could maybe repot it to a container an inch larger in diameter, or maybe even just do a little “top dress” of fresh soil, but hold off on that until spring.