There is no requirement to give police your identity in every single situation. The case law establishes that in most situations a person's name and biographical information does not implicate their right against self-incrimination, so a suspect can be asked his name, date of birth, et cetera. Of course, in order for the police to stop a person they must have a reasonably articulable suspicion of a crime. Police are also entitled to obtain identification from driver's who are stopped for a driving infraction.
This is not to be considered legal advice nor does an attorney-client relationship exist.
It depends on the circumstances. Generally, you do not have to identify yourself. You cannot, however give a false name. If you are driving a car you are required to show a valid DL. If the cop has probable cause to stop you he can ask you your name but you are not required to respond. You may, however, cause yourself much unnecessary grief by not complying to a simple request.
Now here is a good question. Must you reveal your name to police? Well, as the other lawyers have opined, probably not. On the other hand, if you refuse to sign a traffic citation, that's opposing the police and is a crime. And if you are asked for a driver's license and don't have one, or refuse to produce it, that is driving without a license, a crime. So if you're walking down the street and the police officer comes up to you and asks your name, you have the right to say, "Sorry, I don't want to tell you." This is America, after all, and we are not required to have "Papers," the way people are in some other countries and certainly the way it was when Hitler was around. But be careful, because right-wingers in Arizona and other states, including Florida, would just love to pass laws that make it a requirement that you can prove your citizenship on the spot when asked to do so. It would make it much easier to get rid of illegal immigrants that way, but would also make it much easier to make all U. S. Citizens carry an ID card, which is what they really want.