Well, Nintendo doesn't like to use the numbering system much, except that number has any meanings with some sort of buzz worthy trend (3DS - with 3D display, N64 with 64bit) ... so I'm ruling out Switch 2.
Switch Pro - sounds like it's only for Pro gamers and alienating the casuals - and more of a mid-gen refresh...
Super Nintendo and Super Famicom worked well - so I think they probably go with Super Switch. Then again, it's so 90's sounding... but given choice, I think Super Switch would be the one.
But who knows. Maybe it'll be called Zii or Zwitch to aim Gen Z.