"Aya" is Japanese for "silk" if I'm correct. You could call yourself "silky". :) More suitibly, if you are a Japanese girl, you could call yourself "Aya-chan" or "Ayako". People saying your name with the "-chan" added would mean in Japanese culture that you are very close and friendly with that person (family, boyfriend, childhood friend). "Ayako" is just your name with "ko" added to the end, which means child. A lot of Japanese girl names end with "ko", and can sometimes be used to make a little nickname.
Ex. If a girl's name is "Usagi" (rabbit), since "usa" can mean "rabbit" on its own, adding "ko" to the end would create the nickname "Usako" (bunny-rabbit).
Also, you could call yourself "Ayami" or "Ayabi", roughly meaning "silk woven in beauty". They both mean the same thing, so choose the one you think sounds best. :)