Don't have a name for you, but a link. See below...
I bought two of the exact same begonias at Home Depot earlier this spring.
Just loved the foliage! I re-potted them after about a month in a slightly larger blue pot.
Very complimentary! They do bloom with the usual, pink flowers.
Watch the watering---they can, happily, go a bit dry and not complain.
All the tag said that it was a Rex Begonia. There are many kinds--you could Google
"Rex Begonia", then click on "images" (upper left tool bar) and see if any of the images match yours.
I attach a link to a Begonia site. You can learn a lot here from taking care to propagating