I believe the original Go North East livery lasted between 1997 - 2012 as several Go North East buses where still about in that livery in the Autumn of 2012 especially around Chester Le Street.

As for branding it’s always been there ( Wear Express was first used in the 1990s for the original X5 between Hartlepool - Newcastle) along with Superliner ( for the original X1 between Middlesbrough- Newcastle).
The Go Wear buses , Northern, Xpress Coastline names started to go in 2006 to be replaced by Go North East as the official name for them all. I think Tyne Tess express was one of the first as early as 2004 although then just branded as X10 with Fab 56 and Angel 21 both starting the branding in 2006 the likes of Fast Cats then coming in over the following years. Northern came back in 2012 with the all over red to replace what was left of the original livery’s and like said the all over white. This was the case till 2016 when the new livery was introduced with a slight change in 2019.