I asked the Nintendo Support and got this (orig. post):
Dear,
Thank you for contacting Nintendo.
You can only use your Nintendo account on the Nintendo Switch.
The Nintendo account is, however, not the same as the Nintendo Network ID, which you use on the 3DS family systems. These can only be linked to your Nintendo account, so you can use the credit from the Nintendo eShop also on the Nintendo Switch.
If you are using only one Nintendo Network ID, please create the Nintendo account under this link.