When we were trained in Agile Central we set up our Project structure to reflect our Agile Release Train team structure. This seems to be consistent with how the product works, so why is named project. I am continually explaining that is our team structure. We also have non-Agile teams tracking there work there, now that AC is our corporate standard, and they want to know where the project calendars and Gantt charts are to track their projects. It seems that renaming that to team would clarify the usage of AC.
I looked back to try and find some of the older threads where we've discussed this but in short, Project is a legacy term from the very early days of the Agile Central (formerly Rally) product that's pretty deeply baked in. We're all in agreement that it needs to be changed and the CA product team is looking into it, so there's light at the end of the tunnel.
From my experiences both as a customer and now as a CA employee it's inconvenient but very achievable to get your users accustomed to Project = Team, just takes a while to socialize the knowledge. "Release" is a similarly loaded term in AC so you'll want to pay attention to that as well, and rest assured that the CA product owners and managers are working on it. Hope that helps.
You're right Leonard! They definitely are used to organize teams -- here's more about Projects in Agile Central: Set Up Your Teams | CA Agile Central Help
I think they might have been named Projects (WAY back in the day) to use them to organize as projects or teams. We definitely recommend setting up the hierarchy for teams, though.