Resist the urge to name her something popular. I have met 400 cats and dogs and children named Luna or Stella. No. Learn her personality and figure out who she is before you name her. Congrats on having a beautiful new friend!
Currently judging between 2 names based on behavior
The first is the name of my former D&D Artificer, Sharahn. This is because she only wants to hang out around my technology for some reason
The other is Lilliana, like the magic Planeswalker. She's black (super duper dark brown, but close enough) and keeps knocking over my Garruk plush but not my Chandra plush