It is a different deal. One doesn't give an account of events because they want to consult with an attorney first, because anything they say can and will be used against them in a court of law. I can understand that and does not imply guilt.
but one does not need to consult an attorney regarding one's name and one's name has no bearing on future court preceedings.
People do not give their names because they do not want it known who they are for some reason.
J, what you say is very logical, but I'm sure you'll agree humans don't always react logically. For most of us middle-class types, who enjoy pretty good relations with LE over the course of our lives, I think it's hard to understand that some people have a longstanding hostility toward the police and their first instinct is to be uncooperative.
Whether that hostility is justified is another, very long discussion. But there's no question that it exists in some quarters.