Northern should go:
Manchester suburban
Network North West
Where does the distinction lie? If e.g. Crewe and Stoke to Manchester end up as Manchester suburban, and given that they make up e.g. the majority of Northern Wilmslow services, I'd argue that they should, that doesn't leave many for the latter group, especially if Merseyrail moves towards Wigan and Preston and if Settle and Tyne Valley are included with Leeds or the North East instead.
I wouldn't call Scarborough or even Hull a Sheffield suburban route, but I'm not sure where else it would go.
West Yorkshire NSE type thing
Send Nottingham to Leeds over to EMR
Lincoln to Leeds as well?
That would consist of two hourly routes (Hexham and Morpeth) and one route with 2tph (Ashington); I'm guessing that would include all Northern Newcastle and Middlesbrough routes?
Edit: I think one of the only somewhat-cohesive ways to split up Northern would be in three; Yorkshire, North West and North East.
I'd put the Hope Valley with NW, due to Buxton and Glossop facing towards Manchester and, even just east of New Mills, there's 5000 more passengers annually to Manchester than Sheffield. Only Bentham and Carnforth on the Bowland line have more passengers to Lancaster than Leeds, and there's little point in having Carlisle services separate from all other local routes through Shipley so Leeds – Carlisle and Lancaster (/ Morecambe) would be with Yorkshire.
I'm less sure about Calder Valley routes. York – Blackpool North and Leeds – Victoria spend most of their length in Yorkshire, Leeds – Wigan Wallgate's around evenly balanced, and Leeds – Chester spends longer in the North West, but I don't think they should be split up.