If you dont want to just find a similiar, look into the doll face persian.
If you wish and afford to "upgrade" look into Turkish Angora. Beautiful elegant and gracile.
I would also describe the kitty in the picture as a white domestic longhair. Most cats are not any particular breed.
Generally I don't recommend getting a pet as a surprise for anyone, even your wife... A pet is a family member and a long term commitment. What about involving your wife in the decision process?
That’s a pretty cat! I would describe them as a white Domestic Longhair. If you want to find a similar looking cat, you might have luck looking in your local shelter. But if you want a purebred, you can look into a doll face Persian or a Turkish Angora, as StefanZ said. I’d like to add that some more breeds you might like to check out would be Maine Coon, Norwegian Forest Cat, and Siberian. But, I think you should make sure that your wife is onboard before bringing a new cat home.