All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
There is no doubt that the Muslims should be named with good names like the names of Prophets and companions and the like. The name has an effect on the person in general. For more benefit on the conditions of names in Islam, please refer to Fataawa 87262 and 82724.
As regards your name (Zartashia), it might not be the same name as Zoroaster, after whom Zoroastrianism (a pagan religion) was named. The fact that the two names have similar spelling does not mean that they have the same or similar meaning.
Hence, if your name does not imply a meaning that is contrary to the Sharee’ah, then you are not obliged to change it. Moreover, the mere fact that the name is of non-Arabic origin does not make it dispraised unless its meaning implies something forbidden. For more benefit, please refer to Fatwa 127404.
In any case, if you want to change this name because of doubt or in order to avoid any embarrassment that you feel, then it is permissible to do so, Allaah willing.
Allaah Knows best.