白勇语法的一道题目求助

zhang171903992

Several officials spoke to press on condition that they not be named in the story
A:
B: that their name will not be used
C: of not being named
D: that their name are not used
E: they will not be named

答案是A，我的疑问是that引导的定语从句用A来表达不完整呀？没有谓语呀，为什么是对的呢，我选择的是C