It looks like 'Sophie Cecile'. I think there was a post earlier about wondering if this one ever blooms. I thought mine had in the past but don't remember it blooming for the last few years due to it being pot bound. Most people grow it for the leaves anyway.

If you want blooms try 'Dragon Wings'. The best bloomer ever but the leaves are on the dull side. 'My Special Angel' has beautiful spotted leaves and seems to bloom most of the summer but doesn't get very big. 'Silvermist' is a huge cane begonia with silver streaked leaves and light pink blooms and is hard to beat. 'Irene Nuss' is very much like 'Sophie Cecile' but without the silver streaking and blooms very well. There are so many other good blooming canes that you will just have to buy some to try them. Most canes will bloom given the right conditions of light and fertilizer. They do best outdoors for me but I do have some sporadic bloomers indoors as well.

Good luck.

We have a nother one that blooms constantly with lots of blooms on it. It's not as lush as this one but... We're just wondering how to get this one to bloom. We just put it in a larger pot so I don't think that is an issue.

I second what Butch says. I've heard that 'Sophie Cecile' will bloom occasionally given optimum care and good luck, but I've never seen it. The foliage is so nice I haven't minded, and I have a good gardening friend who surely would bloom it if it's reasonable to be able to, but she also says she grows it for the foliage. Well grown it is a really beautiful plant (mine is not particularly well-grown now at the end of winter!) Some more good bloomers are good old 'Lucerna', and possibly best-ever is 'Texas Tea-Sipper', tho' that's a pretty unremarkable plant.