Names are confusing

At my counseling internship site, there are about 10 interns and 2 of us are privileged to have the same name (which, I will not actually be posting since I'm trying to keep my name off my blog). Since we both started our internship around the same time, it has proved to be interesting and entertaining as clients and the people we work with try to keep us straight. 
Case in point...I was meeting a new client for the first time and we had scheduled a 10am appointment. Now, Even though we call new clients, give them our names, and set up appointments ourselves, it isn't uncommon for them to forget who they were meeting with. At 9:30 that morning, I get a call from our coordinator asking whose number this is, I tell her and it turns out my client thought she had a 9am appointment. Our coordinator wanted to help her out by calling her counselor, but since she didn't remember my name, she had to search through her phone and guess which number might be mine. Thankfully, she put the client on the phone,we figured out the mix-up of the time and all was good.
SO here is a girl, who's a bit nervous already, has shown up an hour early and then I walk in right at 10 and hear this conversation happening with the OTHER intern with my name-
Client " I had a meeting at 10 with ___(my name)___"
Other intern with my name- "uhhh...we had a mtg at 10? I don't have a 10am client....I have an 11am client.....???"
Client- ".......????????????????.............."
thankfully, I walk in at that moment and explain that I have a session with her, not the other intern! Both the other intern and the client looked visibly relieved.