EDIT: The Thread Formally Known as Nintedno Account IDs Are Live! Get'em While They're HOT!
According to Wario64, Nintendo Account users can now create user IDs for their accounts. These IDs can be used to sign into a user's Nintendo Account, and, presumably, will be the successor to Nintendo Network IDs. It would be nice if Nintendo would clarify such information, but, you know, Nintendo is gonna Nintendo.
So if you feel that the handle you currently use for Nintendo Network might be claimed by someone else on the Nintendo Account service before you get your grubby mittens on your shiny new Nintendo Switch you may want to act now.
EDIT: Hey, it sure would have been nice if I gave instructions on how to do that. Let's remedy that.
Okay, go to your Nintendo Account page. From there select "User Info" then select "User ID". Just follow the instructions and you're good to go.
Source: Wario64 via Twitter