The Answer Is A Foodstuff , 3 Letters.
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For more on marking an answer as the "Best Answer", please visit our FAQ.Dickens used the earliest-recorded version, in the form of 'check off', meaning to mark as correct in 'Nicholas Nickleby'.
In British English, the words are in effect synonymous; in American usage, 'Check' can also mean 'I agree/that's right.'
In that respect, a name-check is no different from a book-check, an equipment-check, a shopping-list check or any one of a multitude of other possible checks...a situation in which someone reads down a list and marks with a tick each book/item/whatever that is present.
It is so general, that I can't imagine you will find where the phrase originated.