A generic "Congratulations to our winners" with private messages to the winners with contact information would have been better, and avoided the question altogether.
I don't know that you have an issue listing their names. There names are already public on your page because they "liked" and "shared" the status. You can find them in the list if you click on the number next to the function button on the original post, so everybody already knows they entered.
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I can't herd the cats anymore, so I just set up the electric fences and let them fry when they stray out of bounds.