The correct option is D Her / She's
The first sentence indicates possession of name in the subjective sense, hence possessive pronoun "her" is used. In the second sentence, the pronoun is the subject of the verb, meaning, it does the action. Thus, subject pronoun "she" is required. The be verb for third person singular pronoun in present tense is "is". Hence, Option C is correct. The rest of the options do not adhere to this rule, hence incorrect.