Tom.

Her family runs a prestigious greenhouse called "Flordelis", represented by a warning crescent moon (the one in her collar and gardener outfit). They tend to grow rare plants (some even used for medicine), take care of people gardens (usually rich folks) and some grass type pokemons. This helps you understand why she tends to wear her work outfit even outside of her usual "manual work hours", it means to her. 

She had a relatively normal childhood till her parents had a divorce. The mother moved to another island, letting Luna stay with the father, she would never visit or contacted them afterwards. The father meanwhile ended up changing, he became distant, grumpy, just seeking the negative out of things to complain. Around this time, he also inherited the family business that was going through rough times financially. Seeking to preserve the family legacy, work became his obsession, everything else was just a distraction, including Luna. Every time Luna would seek "daddy attention", he would merely demand her to stop being childish and be "useful" and worthy of the family name. (girl was 9y)

 You could say Luna took that message by the heart :), in the years that followed she would attempt a multitude of things to try impress him. From joining competitions to win prizes in order to try impress him, like Math, chess, swimming, cooking etc, she would also make up competitions in her head (like getting the best grades of her entire school). She would manage to achieve majority of these, but not without using some dirty methods, usually by sabotaging or employing some psychological warfare on others.  She even started working at the greenhouse by her own initiative. Her father sometimes would approve, but never quite gave what Luna really wanted. 

This is getting bit long so I'm cutting the yapping, what I'm getting at is these years of chasing "daddy approval" (and how he treated her) is what molded Luna into what she is currently. Her final goal, is to get a academy degree and win the academy tournament, so she can finally shove up her father face she is absolutely worthy of the family name, and command his absolute respect. Of course, she would never admit this to anyone, if you ask her what she is doing there she would just say it's for fun!

To finish I would like to explain her relationship with her main partner, Charlie, the sprigatito she owns. She found them in a trash can during the cold night of a warning crescent moon, still just a little baby. Without even asking for father approval, she just adopted them, maybe it was to show daddy she could take care of pokemons on her own, regardless of the intention, they ended up bonding. After 4 years, they now even share similiar personalities and deep trust between them, It's to the point Luna likes to just let Charlie out of their pokeball 90% of the time. This also means, Luna is also fiecerly protective of Charlie, being one of the few things she actually does have genuine love and affection, she feels she can be "herself" around them.

If you read this far comment "banana head" so you can prove to me you're a real one ;p

That's it for he backstory, now Luna personality is a bit complicated (complex?), I tried to convey in the ref sheet her personality but there is only so much I can transmit with a few words...

A quirk is that she is almost always smiling, regardless of emotions. Her posture she tends to have her arms behind her back too. It can be quite unnerving when she just stares with her smile at you, and she knows, she does this it on purpose-