This happened to me most recently at magfe. Booked Cindy and when I got there papasan told me she just started another appointment and would be an hour wait. Showed my phone, Natasha came and said there was a mix-up. I think since I confirmed my appointment so close to the start time whoever was using the phone didn't relay the info to the other and Cindy was given to someone who came on the spot. I held firm, and to my surprise Natasha pulled Cindy out from the other appointment and gave her to me. Sorry other monger.
Another time at NYAW there was a slight mix-up where I tried to change girls last minute since I was running late and knew Vera had another appointment right after mine. When I show up Sally asks if I'm seeing X girl (don't remember name) so I just said yes. Sally showed me her phone saying Vera so I went with the initial appointment. Looking at her phone there are a ton of messages so I can tell it's easy for them to mix things up, especially when mongers don't have names attached to them. MMS just goes by past messages or sometimes small nicknames.
In any case, my point was that these mix-ups can happen anywhere, especially with so many mongers making last minute decisions. Try to book early, and send a text an hour before confirming that the appointment is still on