From an article published in “Nameh Mah”, September 2005, by Dr. Khosro Khazai Pardis:
“Zarathustra is not a name given by his parents. ZARATHUSHTRA (its real pronunciation) is an epithet (a farnâm in Persian) and not a name. Therefore it is an adjective and not a noun. It means Golden Shining Star (Zara= golden, Thu= shining, Shtra= star).
The epithet “Golden Shining Star” which is a praise expressing great admiration and high esteem and respect was given to Zarathustra by his followers from the days of his youth. It was adopted by Zarathustra himself and used 16 times in the Gathas. This epithet that was used throughout his life over shadowed completely the name given to him by his parents that we don’t know. But what we know for sure is that no one, either before or during his time was called Zarathustra. This single observation is enough to prove that this was not a common name.”
Here are some further ideas: http://zoroaster-zarathushtra.blogspot.jp/p/etymology-of-name-zoroaster.html?spref=fb