The correct option is C We started a club under the name of 'The Bookworms' Club'.
While combining a
sentence with a preposition, it is often followed by a noun or a gerund.
When the given sentences are combined, a gerund/noun follows the preposition.
Option B has used the preposition 'under', followed by the noun 'name'. Hence it is the correct option.
Option A has not used any preposition, instead it uses the verb 'called'. Hence A is incorrect.
Option C uses the present participle 'calling', it does not use a preposition. Hence C is also incorrect.
Option D is incorrect because the answer lies in B.