Only the important, older ninja know of Naruto's heritage: Jiraiya, Kakashi, The Third (obviously), Tsunade, Orochimaru (unknown, but most likely), Obito, I am not sure if Gai knows or not.
The only reason they were not allowed to broadcast this information to everyone in the village is because they wanted to project Naruto from Minato's enemies. We all know of Minato's godly reputation

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Anyway, Naruto is now one of the strongest ninja in the world. I am 100% sure that Minato's former enemies are either dead or no match for Naruto. Unless, or course, Obito was this enemy that everyone was speaking of.
I could see everyone on the field finding out about Naruto's heritage. All it really takes is Minato showing up and Naruto yelling out "DAD!?" in surprise. That is likely to happen if Minato shows up on the field. Upon hearing this people will finally put two and two together, and once Naruto returns back to the Leaf after the war, they will kiss up to him, bring him gifts and beg for his forgivness after treating him like crap when he was a kid

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On a side note, Minato's Secret is greater than Victoria's Secret

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