In case you was still thinking about a full name for Princess Gaia's full name, here's one I thought of:
Princess Gaea Terra Equestira
To explain, Gaea is a another spelling of the name Gaia. Terra is the Roman name of Gaia (And ironically is also one of the villains from The Immortal Game, or Ponies Make War fanfic.) And its a simple and short name.
Just a thought.