Yorkshireman here.
As far as I'm aware, this is an extension of a policy that's been in place for a few years now. As mentioned by others, there is already a strong Yorkshire youth/academy system in place which has always been very Leeds based/biased. This season, Leeds have been taking some of their "home" games around the region. They've played home matches in Hull and, I think, Rotherham as well.
In a lot of ways, the rebrand is the next logical step.
Speaking from a personal point of view, I think this could be great. I never got behind Leeds because as a youth, I hated them. Local rivalries were stoked so I loved beating the Leeds clubs (Morley, Moortown, Garforth etc) and always wanted to see them do badly. The natural extension of this was that I could never get behind the Leeds senior team because it represents all the clubs I used to hate. I hated Doncaster even more, but that's another story.*
The flip side of this was that I was really passionate about the representative side of Yorkshire Rugby. My 1st trip to Twickers was as a child to watch Yorkshire vs Lancashire. Ian McGeechan is paying it very shrewdly in this attempt to tap into some of the passion that is there for Yorkshire rugby.
I really hope it succeeds. Yorkshire Carnegie will be my third team.
On a side note, I wonder what the kit is going to be like. Hopefully the team will wear white.
* Note my dislike for Donny/Leeds was nothing to do with the clubs and how they were run, but purely as a result of local rivalries. It's taken me a long time, but I've got over it now and would like these teams to do well (but not too well!)