I was the person who posted this name. I saw it listed on a baby name site as a variant of
Euphemia. The site claimed that it was pronounced eh-FEM-ee, but I think EFF-eh-mee could be correct too. As for where it comes from, I'm not sure, but it loks to me like the medieval English version of
Euphemia. (Effemy reminds me a lot of
Tiffany, which is the medival version of
Theophania)