Normally, a project in PhpStorm has the same name as its root folder. So the easiest way to change the name of a project is just rename its root folder. However in this case you have to re-configure access to the server so the server root is mapped to the new project root name.
To avoid these additional steps, you can change the name of the project but have its root folder name preserver.
To rename a project without changing the name of its root folder
- On the main menu, choose for Windows and Unix or for OS X.
- In the dialog box that opens, type the new name of the project.