She may have gone overboard but it is irritating to be addressed by your first name let alone a diminutive by someone that you don't know.
“she has every right to ask to be treated respectfully by someone that she doesn’t know. I am also very irritated by someone presuming intimacy when I have just met them.”
Give me a break. People in positions of power may have the luxury to “Demand respect”, but this is an administrative grunt job, her duties are to provide assistance and customer service to constituents. She might prefer Elizabeth and has every right to request that for the future. She has no right to berate, become angry, and then demand she quit apologizing. Geez.......
A polite - “Thanks for your email, allow me to introduce myself. My name is Elizabeth and I am in charge of ....... I will get back with you as to the times and dates of the meeting.
Sincerely,
Elizabeth.
I have never understood people who throw a hissy fit over things like that.