I think in old English e was thought to be pronounced more like a? Not sure. We need a linguistics person on the Q. Eve may have been more like pronounced as ay (like hay) va. In fact in many languages Eva is pronounced ay-va; I would pronounce Eva that way. But, Eve in modern day would be eve in English to most people in any English speaking country. But, consider this, I have this “argument” with my husband all the time. When he sees a double consonant he does not adjust his vowel sound because in his first language, Spanish, the vowels are always the same. If he saw the words Paser and passer he would pronounce them equally, but an American wouldn’t. The e following the single consonant would change the sound of the a. Following the double consonant the a stays the same. This is why English is so complicated. We have rules that are compicated with many exceptions, and we have rules we don’t follow.
An aqcuaintance of ours, race car driver Rafael Matos, when he first started racing couldn’t understand why all the announcers were pronouncing his name may-tos. I told him to either change his name to Mattos, or give them the correct pronounciation written out mat-tose. That how he spells it most Americans will say it incorrectly. He, understandably did not want to change his name. They do now pronounce his name correctly the majority of the time, I guess he got the word out of how it should be pronounced.