I don't know exactly where this name comes from, but our family started to use it with our first puppy Pug dog back when I was a very, very young kid. So, I've used it for about as long as I can remember.

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From an internet search I found the pose is formally called "splotting": https://etcpets.com/what-is-splooting-and-why-do-our-pets-do-it/#:~:text=Splooting%20has%20also%20been%20known%20by%20many%20other

And AI's take on the matter:
"Watching pets sploot is such a joy, isn’t it? It’s like they’re saying, “I’m just gonna relax right here and look adorable while doing it. If you have a pet who likes to sploot, I bet they’re quite the character!"