I love the name Artemis. I was gutted I couldn't use it in the end but also, it wouldn't have been my first choice girls name. In the end I gave the name to a wooden duck I bought on holiday (as you do).I loveeee Thea and Phoebe, also Clio/Cleo but we've got no Greek near our family trees. I'd still use Phoebe and Thea I think as they're not 'obviously' from the pantheon.
I know an Athena and an Artemis, who are both Greek or Cypriot so that seems on brand, but it does sound a bit weird especially if people aren't aware that naming from the Greek Gods is quite common in Greek culture.