hmmmm I think in Europe (non English speaking countries) people might say AH-da, but in all English speaking countries people would say AY-da. If you live in a non English speaking country: I think it would be easy to correct people. You just tell them and they'll remember.
Ada is pretty simple, it's not like you're using Kayghtelynne Rennae or something.
Ada looks much nicer than
Ayda. I also read that
Ayda was a Hebrew name, if so, it is probably pronounced EYE-da in Hebrew.