What was the 'real' name of hawk- eye?

It depends which "Hawkeye" you mean! In the TV series M*A*S*H, his real name was Benjamin Franklin Pierce. In Cooper's novel Last of the Mohicans, his real name was Natty Bumpo. Clint Barton is the secret identity of The Avenger's "Hawkeye", if you meant him. I think that covers all available "Hawkeyes"!