It's been nearly 3 years since I put up a comment saying that it's supposed to be pronounced as me: (e: = long 'e') and, at that time, I wasn't as knowledgeable about how Japanese names are pronounced. For a while now, I keep going back to the subject on how Mei, as a name, is actually pronounced and I feel confident to say that I am wrong to an extent in this particular case. Since many forms of Mei have two kanji with the first being pronounced 'me' and the second 'i,' it makes sense (to me now) that it's actually pronounced me-ee (not like 'May,' which has a diphthong) (compare the word 出居, written as 'dei' or 'idei'). Let's not forget the fact that there are kanji with 'Mei' as the on'yomi pronunciation (in this case, they ARE pronounced with the long 'e') and I did find a few examples on the Japanese Wikipedia of women who have Mei as their name, but written with only one kanji, but with 2-kanji combinations being the norm for this name, even though I wouldn't be able to find any sound examples for those uncommon 1-kanji cases, I have a feeling that their names are pronounced like how the 2-kanji forms are pronounced.
I would like to point out that Mei in Japanese is not pronounced 'me-ee' or like the word 'May.' Since 'ei' is a long 'e' in Japanese, it is pronounced 'me:' (with reference to BtN's pronunciation guide).