Several senior officials spoke to the press on condition that they not be named in the story.

(A) that they not be named

(B) that their names will not be used

(C) that their names are not used

(D) of not being named（A）

(E) they will not be named

我选了C，看了答案后仍然不知道考点是什么。是因为代词指代？难道因为是officials所以不能用their，好像不是吧，还是因为on condition that 虚拟？但是从意思上看我觉得C更好啊。

快帮帮忙。语法狂差，都要考试了。

that是condition的同位语.
not be named是subjunctive mood. 当他是习惯用法记好了: condition that + not be done.