You can indeed change the name of your Fabulous Storyteller.
First of all, please log into your account on the Luniistore.
Connect My Fabulous Storyteller to your computer and switch it on. Click on the round-shaped logo at the top right of the page, then click on My Fabulous Storytellers.
Change the name of your Fabulous Storyteller by clicking on the "Settings" button of that Storyteller and then click Ok.
Are you unable to click on the Settings button? This means that the Luniistore has not detected your Fabulous Storyteller. To solve this issue, this way!