You will need to use Training Center to do this. Once you have Training Center installed:
1. Connect your Forerunner to your computer and power it on
2. Open Training Center
3. If you don't receive a pop up box that reads "New User," please go to User > Add New User
4. Enter a name for the account on your computer (it doesn't need to be the same as your myGarmin and Garmin Connect username)
5. Click the box next to Add a new device to this account
6. If your Edge doesn't appear in the 'Device' box, click on Find Device
7. Enter the new name for your Forerunner in the optional "Nick Name" box
8. Click on OK
9. Select File > Send To Device
This will load the new "Nick Name" to your Forerunner 305.