Some states (21 as i recall) require a detained individual to identify him or herself to the police when detained - the others do not. My state does not make such a requirement, but Nevada does, and NV was the source of the Hiibel decision which pretty much nailed the ID question with the SCOTUS.
From the CA Attorney general:
The U.S. Supreme Court has drawn a distinction between a detainee's duty to identify himself and his duty to answer non- identification questions during a lawful detention. In Berkemer (1984) 468 U.S. 420, 439, the court stated that a detainee is not obligated to answer any questions you put to him during a lawful detention. (Christian (9th Cir. 2004) 356 F.3d 1103.) However, in Hiibel, the Supreme Court clarified that it was not referring in Berkemer to questions regarding identity. The court upheld as constitutional a Nevada "stop and identify" statute and found that a detainee's failure to identify himself could be the basis for a lawful arrest under a companion statute almost identical to Penal Code section 148. (Hiibel (2004) 124 S.Ct. 2451.)Different states have different laws on the matter. However, ALL the states would require a lawful detention before identification would be required.