(A) that they not be namedThis choice concisely expresses the idea of reporters protecting the identities of individuals who speak to them on the condition that their names are not revealed. The phrase "that they not be named" is an appropriate construction that adheres to the standard use of the subjunctive mood, which is commonly employed to express conditions or demands. Correct answer
(B) "that their names will not be used" is not incorrect grammatically, but it is wordy and less concise compared to option (A). The phrase "will not be used" implies a future certainty, while the original sentence emphasizes the condition of not being named.
(C) "that their names are not used" suffers from the same issue as option (B). The present tense "are not used" implies a general statement, not necessarily connected to the specific condition stated in the original sentence.
(D) "of not being named" changes the meaning of the sentence. It implies a general quality or characteristic of individuals rather than referring to a specific condition set by reporters.
(E) "they will not be named" is not in the correct subjunctive form. The sentence requires a construction that expresses a condition, and option (E) does not fulfill that requirement.