Yes, David I am a collector, not a landscaper! My husband calls the yard my 'private botanical jungle'
Tara, unlike my orchid addiction which still has a serious hold on me, I was able to stop after about 10 different types of begonias. They grow really well here as long as you give them the right conditions, and as David pointed out, some of them get really big. So there definitely is such a thing as too many! They propagate so easily from cuttings, I have given away dozens, too.
In your first picture, that one you have looks a bit like Gryphon, but the second picture looks more like my Sophie Cecile. Gryphon has more symmetrical leaves - sort of a deeply cut maple-leaf shape, and are beautiful dark green like that with silver spots. On Sophie Cecile, the leaves are long triangular in general shape, but very jaggedy. Show us another picture in a month or two when the plant's bigger?
I took this pic of Sophie this morning, but the light was too bright and it doesn't show up well. I had a big clump of Gryphons in the ground a few years ago, but they have petered out, not liking the competition from the oak tree roots. Now I sink the begonia plants into the border in big pots so they have a chance to get roots established.
This little NOID fellow jumped into my cart at Home Depot a few months ago. Label just said 'Rex begonia'. It was in a 4in. pot and I brought it home and made 12 divisions out of that pot. This is 2 of the divisions. Cute little shy pink flowers hiding under the leaves.