Is it possible that dogs can blush? Gunner the Great Dane seems to when he is lovingly praised. If you talk to him like a baby and say things like “Oh, Gunner is soooooo pretty” he’ll roll in his back and start rubbing his face with his paws. This seems like it would be a very complex emotion, but I’m convinced he gets embarrassed by the attention.
I think it’s much more possible that, growing up, you gave him positive reinforcement, when he went into that position.
My WAG, you’d roll him onto his back (to rub his belly) and he’d put his paws on his face and you’d start saying things in a baby voice. He liked that.
You taught him a trick. You say sit, he sits, you say roll over, he rolls over, you say ‘oh gunner is soooo pretty’ and he rolls over on his back and puts his paws on his face.
For most tricks you probably gave him a treat as he was learning them. I’ll bet for this one you’d rubbed his belly (and probably still do). Even if you don’t, the attention you give him when he does it is probably enough for him to keep doing it.
It’s not just tricks and rewards for dogs. They do have emotions. Dogs can be happy, sad, afraid, jealous, angry, etc.
While I’ve seen plenty of dogs be ashamed, I’ve never seen one be embarrassed. I’m not sure that they can feel embarrassment the same way a human can.
Dogs are pack animals, and while they do have a complex range of emotions, they don’t have exactly the same emotions that we do. Rolling on their back like that is often a sign of playfulness and sometimes can mean submissiveness. He’s probably happy and submissive and is basically saying “play with me, give me affection”.