In the late sixties, a rumor that the Beatle's legend, Paul McCartney,

i think C is the correct answer. initially i picked B but later on i found C to be correct.

in option C , "had" indicates that death of paul happened earlier and " had been " is used to emphasized that in some point in the past people would come to know that paul is alive and it was rumour.

Can someone please explain it in details, as I think B should be the answer.

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See the sequence of whole incident.

Died,
replaced,
and
began

First two occurred prior to the last one.
Therefore, first two will be past perfect tense and last one in simple past.
C goes on along the explanation.

Though I did it wrong, later I realized my mistake.

arorni
a rumor that the Beatle's legend Paul McCartney had died and was replaced by a look-alike began to circulate among fans
in the above option B see the use of tense keeping in mind the logical meaning of the sentence.
the first part "Beatle's legend Paul McCartney had died " seems fine as clearly this event happened first and paul mccarton is no longer in effect. keep in mind that we use "had" to show the event or action happened earlier in past than the other event or action in the past But in second part "and was replaced by a look-alike began to circulate among fans" give a impression that his look-alike replaced him
and this thing began to circulate among the fans. there has to be a time in past when people or his fans came to know that Paul was alive since it was the rumour. see the logic author wants to convey through the sentence. there is timeline between two events. hence we are using " had been " to convey that logic.
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Thanks for the explanations...