I prefer this name be pronounced as Eye-da rather than Ee-da, mainly because Eye-da sounds more regal to me than Ee-da. The second reason I prefer Eye-da over Ee-da is because my good friend Ida pronounced her name as Eye-da. The last reason I prefer Eye-da is because Ee-da to me sounds like a mispronunciation, Ee-da to me should be spelled as "Eda", but even then Eda is already a name and from what I know Eda isn't pronounced as "Ee-da".
Much prefer the English pronunciation "IE-duh" to "EE-dah". "EE-dah" is the ubiquitous pronunciation across Europe, whereas "IE-duh" is unique to English-speakers and has lots of quaint British charm.