Recently I started a new job and I have a coworker that keeps using my name in emails. They sent an email that said, I'm going to go out on a limb and volunteer "My name" and raise my hand for me.

I told them this in a private chat: Hi, Can you please never again volunteer me for anything. You can ask me. You were in the military right? That's Standard. My supervisor is the only one that can volunteer me, and that ain't you.

I then took a screenshot of what I had said and sent it to my new supervisor.

How inappropriate do you think my response was?