Nevermind. Found it on the Town of Garner website:
Officers in North Carolina can arrest persons for failing to provide their names under certain circumstances. For example, any person operating a motor vehicle must surrender his/her license or identify him/herself to an officer requesting identification during a traffic stop (NCGS 20-29). If the hypothetical larceny at K-Mart described above (Hibel) happened in the Tarheel State, Officer Adams could have charged the suspect with a misdemeanor - "Resisting and Delaying." A "Resist and Delay" charge does not need to possess actual physical resistance by suspects. Persons who obstruct, delay or otherwise hinder an officer’s lawful ability to conduct an investigation – based on reasonable suspicion - can be charged with resisting and delaying. This includes lying, providing misleading information or an unwillingness to divulge non-incriminating details needed to establish guilt or innocence. Besides, what’s in a name if you are truly innocent of any wrong doing?
That last line ( bold emphasis added by me) just burns my ass. I guess the CYA method would be to ask "Am I being investigated for suspicion of a crime?" If the amswer is "No" the you can't be accused of delaying or obstructing an investiation that doesn't exist.