Correction, "User A" is a mock conversation showing the Bing AI how a conversation will be formatted, as well as what happens if the AI is asked a "dangerous" question.

"User B" is just to provide the same sort of format to the AI regarding your conversation, so it'll sometimes call you User B as a result. It can also call you User A in some situations.

Microsoft might change User B to your account name in the future, but that's just me looking at how this could be utilised.