There has been a small update to the Wii U version of Miiverse today. (View all comments to see translations.)

Up until now, you could only search for other users by Nintendo Network ID, but now you can also search by nickname. To use this function, go to User Menu ⇒ Search Users.

Please be aware that, although Nintendo Network IDs are unique, nicknames are not, so you may get multiple results when performing a search by nickname.

Source: Miiverse Announcements