The daily NYT Mini Crossword shows its appreciation for happy pups with the clue "A fitting name for a dog that likes to run free", and I earn a cookie for solving this one like a good boy.
Catz 'n Dogz – Cercedilla (Intro) | Technostation
Dogs aren't called man's best friend for nothing, although my cats wouldn't agree. However, cute pooches are in the three down clue for the July 17 NYT Mini Crossword game, and the answer is pretty simple.
That completes my usual series of hints. If the clue still eludes you, the answer and reasoning below are taken off the line.
The word you are looking for is "ROVER" because it has a dual meaning for the clue. First, Rover is a common name for a dog, and it goes back many decades, along with other classics like Fido.