While setting up the iPad mini for the first time, you will be asked to enter a name. This name stays as a default. If you want to change this name later this can be done by following the below steps,
Go to Settings -> General -> in the top you will see the name of your iPad which is given during the initial setup. Now tap the Name field, here you get keyboard to type the name. Type your desired name and click Done button from the keyboard. The name for you iPad gets changed.
Here are some screenshots,