I'm under the impression that
Adelaida is pronounced AH-del-EYE-da (-ah-EE-da). So
Aida (EYE-da; ah-EE-da) would be the natural nickname, and
Ada (AY-da) would not really work. I could see
Adelaide nn
Ada, because
Adelaide has the English prn with AYD at the end. I don't like the way
Adelaida sounds if you prn it Addle-Ayda. But I like
Adelaida, and
Ada. I don't really care for
Adelaide because of the sound like addle-aid or add-a-laid.