I tried finding where to add pictures but wasn't able to here they are.

Yes it is a Begonia, perhaps an Angel wing.

Nice plant, yes it does need more light. Not good at identifying particular varieties though.

No need to worry about soil fungus. They are present in all soil containing organic matter (bark, peat, etc) and are harmless. Sometimes they are visible like you have but most often they are there but not visible. You can pick it out if you do not like the look of it.

But it is an indication that you are leaving your mix wet too long. Go easy on watering and let the top dry out between waterings. The fungus will disappear and the plant will be happier with more air available to the roots.

It looks similar to my Begonia Angel Wing Lucerna. Yes they need more light. It is one of the plants that can grow tall and scraggly over time. I have found trimming and making cutting, give the plant more growth. It will get fuller with more stems growing. I have one that got huge see if I can find a photo of it.

leaves have a red tinge while outside getting morning sun, cutting took that are inside are green coloring.

come spring.. propagate it.. make some new short healthy plants ... and then set momma aside... and see if it resprouts way down low.. after you cut off all the pieces for propagation ... [and if it does... it might be time for a repotting.. if its been inn that media since you got it ...]

and then grow them outside... in full bright shade ... until you have to bring them indoors for winter ...

the longer you have it indoors.. in a given year.. the harder it will be.... to maintain a nice looking plant ... it really isnt a long term in the house plant... imo ... as all the heavy bloomers seem to be ... the more blooms.. the more light they need ....

ken

https://duckduckgo.com/?q=Begonia+Angel+Wing+Lucerna+propagation&t=ffcm&iax=videos&ia=videos

why are all the pix purplish??? .. if you have some type of grow light.. it probably isnt close enough to any of your plants.. to be making much a difference ...

and if it isnt a grow light.. maybe its time to take down the xmas lights ... lol ...

ken

The biggest thing you have to worry about is powdery mildew which usually occurs in cool, damp places (fall through winter). Keep the soil on the drier side as this seems to help keep the mildew spores from spreading like wildfire. Else spray the leaves and stems with a good fungicide if you see evidence of the fungus spreading.

I keep most of my begonias under cheap shop lights in winter 12 hours a day and they do fairly well. The rest are nested around plant shelves and get what light they can capture.

blooms of B. convolvulacea hanging down from upper shelf.

Unknown big polka dot cane begonia that only gets what sunlight comes through the double basement doors.

B. 'Teen Angel' on floor next to a plant shelf.