The female name Megan was originally Welsh, though based on Meg, the English and Scottish short form of Margaret and a doublet of Mag, as in Maggie.
In Britain it is almost always pronounced ˈmeɡən, with the DRESS vowel.
Why, then, in AmE does it tend to be pronounced ˈmeɪɡən, with the FACE vowel?
I suppose the answer is that it is vaguely perceived as Spanish, or at least foreign, and that AmE tends to map Spanish e onto FACE. Compare Pedro, Spanish ˈpeðɾo, who becomes ˈpedrəʊ in BrE but ˈpeɪdroʊ in AmE. Alternatively, if thoroughly anglicized, Spanish e can be mapped onto iː (FLEECE), as in Toledo, OH and indeed San Pedro, CA, pronounced even by its Hispanic residents as sænˈpiːdroʊ.
Does anyone pronounce Megan as ˈmiːɡən, which I give as a third possibility in LPD?
The Renault Mégane car is usually pronounced məˈɡæn or meˈɡæn in BrE. I doubt whether it is widely known in north America.