It was my understanding that when a citizen asks for an officer's name and badge number, they're required to provide it to you (in Michigan). Is there a law pertaining to this? If so, is it only the case if I'm being detained, cited, or arrested, or any time I request?
I can't prove a negative, but it seems quite clear from my research that providing name and badge number is policy, not law. i.e. Many departments have a policy that their officers will provide name and badge number on request, but the punishment for failure to do so would be at the employment level not the legal level.
This site has a fairly good selection of various police department policies
I will note that Massachusetts appears to be an exception as mentioned by jimsug in his comment to another answer, they do require police to carry and show ID upon legal request (I did not look up what a "legal request" is)
Contrary to the myth, police are not required to identify themselves as such, unfortunately.