It doesn't seem to matter too much, though Denethor would realize Aragorn's background, I don't believe Faramir is a learned or (obviously) as old and wise as his father, and of course, he doesn't carry a Palantir around with him. A name is a name, and without a person attatched to it, I don't think that "Aragorn" would be all that important to Faramir.
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