There are now DNA tests available that can pinpoint what your dog might be genetically. Some companies can only do 30 or so breeds but most advertise well over 150.
Why should you care - well it is a way to know what sorts of things healthwise you should be on the lookout for as many breeds have unique health issues. I was at the vet last year and there was a puggle there with an eye issue - the owners shared what it was and it is common in beagles. They then went on to say that they had trouble with the other eye before and it was an issues specific (although not exclusive) to pugs. So much for hybrid vigor.
Darling picture though - good luck