Correct Option E
Original sentence:
When a man appeared in the village of Artigat in the summer of 1556
and presented himself as Martin Guerre,
only a few locals suspected whether he assumed the identity of the man who had disappeared eight years earlier.
Elimination Process :
1. Whether - Redundancy with word suspected.
Whether - it means "expressing a doubt or choice between alternatives", it usage is as a conjunction, which here is not required, as sentnece indicates single condition, through word "suspect".
Suspect - it means "doubt the genuineness or truth of"
Elimiates - A, and B
With D - "his" - is a possesive pronoun, used to show ownership, and present participle "assuming" for past incident, demeans the meaning, additional "assuming" is not parallel with other past tense verb. - eliminate D
(A) whether he assumed
(B) whether he had assumed
(D) his assuming
Remaining with (C, and E)
(C) he assumed - simple past tense
(E) that he had assumed - perfect past tense
C, and E - both express completed actions that took place in the past.
We use the simple past to say what happened in the past, often in sequential order.
The past perfect expresses events and actions that occurred prior to another past action (usually expressed in the simple past, like "assumed").
Some indicators for past perfect tense can be used - already, up to then, before (that day), after, once, earlier etc.
Option E : gives fulfills the intended meaning with perfect past tense, and essential information with "That" usage.
Events like "had assumed" parallel with "had disappeared" makes the sentence - Correct E