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That depends on the OS you're referring to. In Windows Phone 8.1, go to your phone Settings > swipe to Applications > Cortana > you will be able to change your name there.
In Windows 10 PCs, click on the Cortana icon in your Taskbar, click on the Notebook icon (a rectangle with a circle in it at the left side of the screen), then click on "About me" - you will be able to change your name there.
You may create a Windows Central account to respond in this thread, and it would be helpful for you to be careful in typing next time, especially when you're typing your name in Cortana.
10-21-2015 05:17 AM