Catmom and I have been working on a theory!
Guessing this pup:
As Yugi's.
Yugi has made quite a few references to water. Both the yugioh cards mention an ocean or waterfall. The song in their sig mentions waterfalls as well. On top of all that, Yugi has made comments such as, "keep yourselves afloat!", "you've all made leaps and bounds when it comes to deciphering the waterfall of hints the staff has left for you this month!", "Hopefully things will become crystal clear as calm waters soon~".
This pup has a few qualities that imply it's water related. The crab shows that if not in the water, the pup is at least near water. The markings on its face also look very much like scales. Of course, it has quite a few features that make it look like it's got nothing to do with water, but I think that will change.
Yugi also made this comment: "my dog has obstacles to overcome before they can reach their desired goal too!"
I'm thinking maybe the obstacle is that the pup can't swim or live in the water yet and that might change.
Yugi also stated, "Time for me to stop being my usual super shy turtle self and climb outta my shell, huh? x)"
The turtle comment could be a more general water hint (or something we're missing yet) but the could reference the crab as well. They're both aquatic/semiaquatic creatures and they both have shells of sorts.
Catmom and I also looked through yugioh cards to see if there were any that seemed to relate to the pup/hints but didn't find any that particularly stood out to us.
We also briefly discussed
this pet of my namesake being another hint since it
technically has another water reference and was one of few pets named, but we weren't sure whether it was just a coincidence and yugi had gotten it with that name.