That's understandable. There's no real need to, after all, like you said.

[Mars takes out another parchment and writes out her full name to show Fenimore. It's a little longer, 火野 レイ, a total of 4 characters. She points to each in turn.]

Well, my family name, Hino, means 'of Fire'. And my given name, Rei, means either Spirit, Beauty, or Companion. So, my name, depending on how you want to view it, could be Spirit, Beauty, or Companion of Fire.