In Arizona the law states that you only have to give your full name.
Let's imagine someone suspicious is hanging around a vacant storefront and the LEO thinks they're casing the joint (a la Terry v. Ohio). The LEO has reasonable suspicion to detain him. The LEO asks the person to identify himself. He complies and with a heavy accent gives his name as Juan Gonzales. He declines to furnish ID. A frisk doesn't reveal any contraband.
The LEO observes that in the strip mall where the stop took place there is a Home Depot and illegal aliens regularly gather to solicit work as day laborers. In conjunction with the man's ethnicity and accent this enables (requires?) the LEO to ask the man about his citizenship status. As is his right, the man refuses to answer any further questions. Can the LEO arrest him?
I'm reading over the law again and it says, "a reasonable attempt shall be made, when practicable, to determine the immigration status of the person." We know that if you're driving you are required to present a drivers license, but in any other situation, what happens if you refuse to answer immigration status questions?
Lets say that the LEO arrests the man. Eventually it turns out that Juan is a US citizen. Were his rights violated?