You are correct, the official moniker is Bf-109, but the Allies referred to it as the Me-109.
BTW, since we are Birds of a Feather, I bet you'd like the movie "The Blue Max". It's really hard to find on bluray, but worth it! The flying sequences are first rate, and no cgi.
point of trivia: Messerschmitt, yes, but Bf-109, produced by Bayerische Flugzeugwerke.
you don't want to get your flugzeug works confused