Deny consent to search -- why doesn't this apply to disclosing one's name?

Police are afforded the right to lie. Why isn't the public granted the right to silence?Scott Henson talks about a TX bill to ban consent searches. It's interesting go read it. Essentially, if someone is denied the right to refuse, then they aren't really being given their rights.

Now, for the larger issue. Remember that cowboy in Nevada who refused to identify himself? Same thing with consent.

Why, if it might be inappropriate to not have consent searches [because can't deny someone the right to refuse], is there not also the clearly established right to refuse to identify oneself?

I see no difference between the consent searches and the identification standard. And I'm amazed that LE seems to agree that "nothing is found" in re car searches, but put up a fight about the ID-requirement.