You should never lie. Our laws know that in order for a policeman to perform his duties, he needs accurate and appropriate information. When a police officer asks for your personally identifying information while giving you a ticket for a wrong doing, you need to give them the correct information. This is most likely done through your identification card and/or drivers license.

If you gave a police officer false personally identifying information through a false I.D., and you forged that I.D., then you committed a crime by violating A.R.S. 28-3476 [Falsification of license]. If you did not make that I.D., but are still using it knowing it to be false, then you committed a crime by violating A.R.S. 28-3478 [Unlawful use of license].

If you told a police officer false information aobut who you are, then you probably still committed a crime. Under these circumstances, a police officer or prosecutor could charge you with a violation of A.R.S. 13-2907.01 [False reporting to law enforcement agencies].

If you gave a police officer false personally identifying information by mistake, then you may not be in trouble. You would, of course, need to contact the officer or prosecutor immediately upon realizing the information you provided was inaccurate. This would further your position that it was just a mistake, and not intentional.