1. Prevent Family and Loved ones from being associated with you and thus become targets.
2. Some people just prefer to keep out of the public eye while still doing good acts, i.e the man who pulls someone out of a burning building and doesn;t hang around for the press to tell him he did good, simple knowledge that he did being enough in itself.
3. Keep media Circus away from you, if you beat the bad guy and then are on every TV or Radio and everyone knows where you'll be and where you'll live how will you ever be able to get the jump on the bad guy.
4. Prevent any complications with socail life, such as friends suddenly worshipping you because your that guy in those lovely spandex pants..oh your so yummy.... But Sue i've known you since I was 6 and just don;t think of you that way!
5. Becoming public knowledge means fans, hangers on, flunkies, stalkers and all manner of other civilians who will follow you about and thus potentially be in the line of fire should a villain show up.
6. The typical Super Famous attitude of "Hey when I'm in the spandex fine i'm public property, but when they come off my lifes my own leave me be"! where the famous want some time off, time out etc without people adoring them all the time.
7. You may be a villain or redeemed criminal trying to do good, your identity becoming public knowledge could compromise and complicate that when the Avengers start trailing you everywhere in order to bring you to justice. i.e "But I was waiting for the robbers to come out, not casing the bank!.... sure you were Captain Chaos....sure you were".
8. You may not be a very human looking super hero, Marvel is a great example of this where a huge anti mutant sentiment exists..... and ties back in to number one above, but also if you were a normal kid, who mutated into some five headed eight eyed gimpoid, would you really want people to know who you were...
9. Prevent complications with work i.e "Say mr giles I was wondering if you were going to let me know about my six monthly pay review?........ sure Mr Chaos just don;t cursh me like a tin can anything you want, how abut a 200% raise and a corner office with a window?....say isn't that yours?"!!
10. to avoid complicating what your doing.... I mean not every hero is out to save the world, a lot are just out to protect thier little corner of it, or sjimply remove all drug dealers, or pimps or whatever.... if people know your a super hero, suddenly you'll be bombarded with every request under the sun from stopping the school bully, to getting Mrs Clarks cat Tabby down from the tree....all of whcih will eat into your serious hero time, and if you turn down the peoples little requests...your name suddenly becomes mud and you get villified.
Basically someone with a secret Identity is free to do good without complication, though often at the sacrifice of reward and acknowledgement. whereas someone with a Public Identity has to keep in good with the people and the press and find time to do good, making Public Relations an absolute must, which means having to spend time opening malls, visiting hospitals, kissing babies...and all the rest of it in order to keep your adoring public and generous patrons happy.