Xcode provides users with the option to rename the project. You can do this in Xcode 6 and Xcode 5 by following the below mentioned steps.
Navigate to Project Navigator, select the Project. After entering the new name for the Project, press Return on the Keyboard. In this example, I am changing the name of project from StopWatch to MyStopWatch.
Once you press enter on the keyboard, the following confirmation screen will be displayed. Make sure you are Ok with the displayed changes then click Rename option.