I like Nate too, and given your first boys have yours and your DH's initials I think its a nice touch to continue the theme.

Just on Taye - I have nephews called Taye and Tyson, which is shortened to Ty. Not sure if you shorten your T yron to Ty, but calling Taye and Ty gets pretty confusing when they're cousins, let alone when you're doing it all the time as siblings.