The correct option is
B my/you/me
In the first clause of the given sentence, it is clear that an adjective pronoun must be used.
A possessive adjective or adjective pronoun is usually used to describe a noun, and it comes before it, like other adjectives.
The only adjective pronouns that will fit into the clause are 'His' and 'My'.
We can thus eliminate options A and D as incorrect answers.
Since the speaker is talking to another person, second person 'you' must be used.
The options that satisfy the conditions are options B and E.
Option C is incorrect.
If the first adjective pronoun is 'his', the third adjective pronoun must be 'his.' Option B does not satisfy the condition and thus it is incorrect.
Hence the complete sentence must be-
My name is Samuel, but you may call me Sam.
Thus option E is the correct answer.