After much research and deliberation, I have decided to name my guitar Cadence, or Cady for short. A cadence is "progression of at least two chords that concludes a phrase, section or piece of music" to describe it simply, so it's musical origin fits a guitar. Plus, when you shorten it to Cady it becomes one of my favourite names :)
I considered Hathor (egyptian goddess of love, music and beauty), Euturpe (one of the nine greek muses; the muse of lyric poetry) and Asteria (greek mythological name meaning "star"). In the end, I didn't like the first two names and Asteria didn't really seem to fit my guitar. Cadence just popped into my head and ta-da! Cady was named.