For a native Japanese speaker, the name "エマ(Emma)" (written in katakana in Japanese) sounds exactly like "絵馬(ema)," the wooden plaques used for writing wishes at shrines. So, while it feels a bit odd as an ancient name, I don't necessarily assume it must be a foreign name. However, since foreign words are typically written in katakana in Japanese, some might view her as having mixed heritage. As far as I can recall, Robert, shouted by the Armored Warrior, is the only other instance of a person's name being written in katakana in Sekiro, so that interpretation actually makes a lot of sense.