I see that Begonia 'Pin-Up Flame has semi double flowers.
I'm still confused Janet, sorry,
as the Science Image library is the ONLY one that has the exact match and name it : Begonia tuberosa 'Pin-Up', do you mean they don't use the right name, but should change it to Begonia 'Pin-Up' instead like in RHS, while the picture of the plant there has obviously dark glossy leaves?