When we say identity conflict, this is a kind of conflict displayed by a character when the identity that he or she has chosen has resulted into different problems. Based on the dialogues above, the one that shows this is option B. Hope this answers your question.
Answer: B) "Don't call me a 'millennial,'" I spat out the word. "I'm not like my peers, who post every sneeze on social media, thinking the sun rises and sets on them."
Explanation: in literature, a conflict is a struggle between opposite forces, usually between a character (the main character or a very important one) and himself (internal conflict), society or another character (external conflict). An identity conflict is an internal conflict, and from the given options, the one that expresses an example of this kind of conflict, is the corresponding to option B.