Create a new Nintendo Network ID

Linking your IDs is permanent. Additionally, deleting the NNID will delete everything.
Deleting a Nintendo ID
This includes licenses and wallet balance.

Unlinking your NNID from your Club Nintendo account may be possible. These are the steps taken from a call a customer had with a Nintendo Representative regarding the issue:

1. On the Wii U Menu, select the Nintendo eShop icon.

2. Select "Menu" or press the Y button.

3. Select "Settings/Other."

4. Select "Club Nintendo Account."

5. Select the box under "Club Nintendo Account," and enter your user name, and then select "OK."

6. Select the box under "Password," and enter your password, and then select "OK."

7. Select "Link" to link the Club Nintendo and Nintendo eShop accounts together.

8. To unlink a Club Nintendo account, follow steps 1-4 above, then select "Remove" twice.

Original can be found here.

If you really want to change your name, I’d say your best bet is to call Nintendo.