AITA for discouraging someone from using their name because it's my name

I was part of a project at work. There were about 20 of us collaborating on this across several offices so pretty much the entire project was via Zoom, Slack and email. The entire time I was the only "Kate". I knew most on the project with only a handful of new names, one being ""Megan"".

Come the end of the project, we all get together for the first time and I put my hand up for organising some team events/dinners. Megan came up to me and offered to help with planning. I said all that was really left was to make a booking for dinner on the third night. Megan said she knew a place. Jump to that night and we all arrive at the restaurant. I asked Megan "what name did you put for the booking?" To which she replied "Kate." I smiled and said "Oh you didn't need to put it under my name." And she said "I didn't. Kate is my name."

I seriously had a mini freak out thinking I had been calling Megan by the wrong name the entire project. I tried to clarify "Oh I'm so sorry I thought your name was Megan. That's what's on all the company stuff." She huffed a bit and said "Megan is my legal name but everyone calls me Kate." I was very confused and tried "Oh is that like a middle name you prefer to go by because you can tell HR that and they'll change it on record." "No my name is Megan but I just don't like it so I go by Kate." At this point I was so confused so I just went in and sat down, away from her, for dinner.

The next morning I saw Megan and said good morning. She snapped at me that I should say "Good morning Kate" since I know that's her name. I took a breath and replied "Well we're at work now and everyone knows you as Megan. I've been the only Kate this whole time so it would be very confusing now to suddenly have two Kates." She huffed at me, called me a rude bitch then stormed off.

Later on another colleague asked me what was going on and I explained it as above. They said "Well if she said that's her preferred name we probably should respect that even if it's just for two days." I just said "first Zoom call everyone did a quick intro bit. She could have said "Hi I'm Megan but please call me Kate" back then and by now we'd have some distinction between us. But she basically sprung this claim to my name out of nowhere and I'm the bad guy for not wanting to muddy the waters of what work was done by Kate and by Not-really-Kate." Colleague just shrugged, said it was all a bit petty then we went back in to work. I agree it's petty but I also work hard and want to protect my recognition.

Project went well, everyone was happy and at least for now I have no reason to speak to Megan. It's still sitting weird with me that right before presentation time she decided she was also Kate. We did very different contributions to this project and it makes no sense to me to start confusing things by suddenly having two Kates. AITA?