hmmm... I never thought of pronouncing it EE-da before, I kind of like it like that. A little girl named that... would be cute. However, to clear up the mispronounciation thing I think it should be spelled Eida.
Marie,
Josephine,
Lynn,
Denise,
Olivia,
Diane,
Lilly,
Daphne, and
Alexandra could make good middle names.