Nope, it's not short for Margaret. Although when I'm out at a bar that is usually my go-to fake name. That or, "Charlie. My parents named me after my great grandfather who invented velcro". Depends on the mood I'm in and how good I am presently feeling about my poker face.
No unnecessary vowels. No extra consonants. No story about my parents thinking the name would sound distinguished when it followed the prefix "Madame President". Nope. Megan . Just Megan.