Welcome to GT!
One of my girls is also called Luna. She's my very shy girl, but is also a wild child and loves to play with stuffies. While she enjoys the occasional tug-of-war match, she prefers to play alone and prance around with her toys. My other hound, Nova, is not as enthusiastic. About once a month or so, she'll get a little silly and pounce on a toy, but other than that, she's super docile. Your Luna might never play like a typical dog would, but I don't think that it directly correlates with happiness.
Enjoy every moment with your new pup! It is so much fun to watch them come out of their shells, especially with the shy dogs.