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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
The basic ruling regarding names is permissibility. Nothing of them are prohibited nor disliked except what implies a meaning that entails prohibition or dislikeability, such as the names that imply enslavement to other than Allaah The Almighty and are thus prohibited, or the names that imply commendation and are thus disliked. The name "Aayah" does not imply a meaning that is Islamically prohibited and thus there is nothing wrong with using it as a name.
Aayah linguistically means "sign" and everything in this universe is one of the signs of Allaah The Almighty that indicate His absolute power and greatness, and humans are one of those signs.
Finally, it is more appropriate for the Muslim to choose for his children the names of the Prophets, and of the male and female companions and righteous predecessors. For more benefit, kindly refer to Fataawa 82724 and 87262 about the general guidelines regarding naming a newborn baby.
Allaah Knows best.