Tweet is the name my Dad gave to me when I was a little girl.   He called me his little Tweetie Bird and the name stuck for the rest of my life.   The Family originally spelled it "Tweetie", but a lot of people spell it "Tweety" because of the cartoon character.   Who knew?

I don't mind either way, but for the sake of avoiding any confusion, I usually just call myself the name the family mostly use: