You can't change your Nintendo Network ID on a 3DS. Nintendo Network IDs are linked to your Nintendo Account, and you can only change your Nintendo Account ID on a computer or mobile device.
Here are the steps to change your Nintendo Account ID:
- Go to the Nintendo Account website: https://accounts.nintendo.com/
- Sign in to your Nintendo Account.
- Click on "User Information".
- Click on "Edit".
- Enter your new Nintendo Account ID.
- Click on "Save".
Your new Nintendo Account ID will be reflected on your 3DS after you've made the changes on the website.