If you are one of those people who used the passport and visa of another person to enter the United States legally, used another name(s) while here, or assumed the identity of an American citizen, have documents that are in several different names, or some other situation in which you have used multiple identities, you have a very messy situation to adjust your status to Registered Provision Immigrant (RPI) legal status as part of the Border Security, Economic Opportunity, and Immigration Modernization Act of 2013 (BSEOIM).
So let us assume that you came with a passport and visa that belongs to someone else (by the way that is a serious crime and deportable offense under US law) and if you were fingerprinted at the airport, as far as the United States is concerned, that is your identity and there is no way you can change it. Now, if you can provide evidence of being here by 12/31/2011, prove continuous presence, have not committed a felony and no more than three misdemeanors, meet other requirements like paid taxes if employed in the past, and file a completed application -- assuming that USCIS does not insist on looking at original birth certificates as it does for green card applications -- chances are that you will be approved with your new identity.
The problem will come for those of you who entered with one name and then used one or more names to live your life. So if you entered USA as John Doe, and your real name is Harry Doe, and then worked as Mark Doe and rented an apartment as George Doe, you may have a hard time putting a complete application together. In all cases of using forged and/or fraudulent documents and identities, it is best to consult with an attorney.