Hey there gabemst3k! Glad you asked about the display properties on the Intensity III. My youngest son has expressed an interest in a device very much like it, and since he's of that age, will want to see the name of his contact appear in that list rather than the number. Just like most VZW devices, the name of a contact will appear in any activities list (call logs, message logs) whenever available.
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gabemst3k, if your question is based on one of the reviewers commenting on the name not showing, I read that, too. And I think that person either didn't enter the numbers with the area code first, or maybe there's a setting to show numbers only. I feel confident this phone would show the name, as Dion replied above.