What will happen to the "Wii something" games when the NX comes out?

[Never]

With the DS, Advanced Wars stayed Advanced Wars in the west and was called Famicom Wars Ds in Japan.

I see no issues with them just using the Wii name for games like Wii Party and Wii Sports by naming them Wii Sports NX and, as I pointed out, there's precedent for them naming things like that.