Is it obligatory to fast three days as an expiation for an oath (kaffarat yamin) for someone who swore not to imitate anyone in a haircut, meaning by that not to tell the inquirer whom he imitates?

If you swore falsely that you would not imitate a specific person in your story, this is considered a "Yamin Ghamus" (a false oath taken intentionally), for which repentance is obligatory, and there is no expiation for it according to the majority of scholars. However, if you wish to be cautious, you may offer expiation for an oath by feeding ten poor persons, or clothing them, or emancipating a slave. Fasting is not sufficient unless one is unable to do any of these types of expiation.