What is the punishment for illegal immigrants using fake names?

It is a very popular trick among undocumented aliens to use assumed names (sometimes after stealing an identity) to hide their real identity or to hide their criminal past or just to keep their real identity from having any paper trail in America as long as they are in the country illegally.  Lawfully speaking, using a false identity is a crime, especially in a legal setting.  So for instance, if you file a tax return with your fake name, you have broken the law.  Similarly, most transactions that you might engage in without thinking, for example with a bank or car dealer or credit card company or utility provider, have clauses that clearly make it illegal for you to use a made up identity.  It seems that many people who benefited from fake identities in the United States will pay a very heavy price when it comes to taking advantage of Obama Amnesty which requires that even as an undocumented alien you provide a lot of documentation proving your entry into the country or that you went to school here or had jobs or owned/rented homes, etc.  If you lived your life under a different name but your birth certificate and passport have your real name, you are out of luck with the amnesty.