Sentence Correction

Several financial officers of the company spoke on condition that they not be named in
the press reports.
A. that they not be named
B. that their names will not be used
C. that their names are not used
D. of not having their names
E. of not naming them

[spoiler]OA: A;
Fine. 'A' is subjunctive form.
But I can't figure out what is so wrong about 'E'[/spoiler]

spoke on the condition that (followed by the condition)

condition of is inappropriate in this context

"condition" is in non underline portion that demands a subjunctive mood.

hence A is correct