You have separate heroic and secret identities, and a very good reason to keep them apart. This can be a personal hang-up, or it may be because you have friends and loved ones you do not want involved.
It is a bother for you to change between your secret and super identities, and you must occasionally take steps to protect your secret identity. Some people may have a relationship with you both in your super and secret identity, which is confusing. If your identity is discovered, you will go to great lenths to protect it, making you sensitive to blackmail. If it is finally made public, you must pay off the limitation.
If your secret identity has a demanding life, that requires you to spend time sorting out these problems, this is worth two limitations. Examples include a loved ones to care for, a job you must spend a lot of time on, or demanding financial obligations. However, check with your GM on this; an involved personal life might not fit the theme of the campaign.