I agree with elbowin on Dacota (f)/Dacotus (m). Dakotai, as Sabertooth suggested, wouldn't be logical, that sounds more Greek than Latin.
Since the Latin language doesn't use the letter "w" (at least not frequently) Dawsoni wouldn't be a great option. elbowin's suggestion is possible.
However, I'd like to add that Dawson means "David's son". David translates to David in Latin, and since Romans usually named their sons after themselves (more info on Roman names here:
http://www.behindthename.com/glossary/view/roman_names) I'd just call him David. It might not be a precise translation, but it's historically correct.
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I know, it's all horrible teenage angst.