No terminology referring to geography in Ireland is neutral when used by people in Ireland, or by British people who know something about it. I studiedly only ever use the terms 'Northern Ireland' and 'Republic of Ireland', and never terms like 'The North', 'The South', 'Ulster', 'The Six Counties', 'Eire' etc. To do so is to give away your views on partition, even if only inadvertantly. I have sometimes bizarre conversations with my in laws (in Dublin) who always refer to NI as 'The North', and I always say 'Northern Ireland'. This has been going on for years and everyone tacitly accepts it and never comments or attempts to correct. For the problematic city in the North West I have evolved the strategy of always saying 'Derry' and always writing 'Londonderry', as the latter seems more formal (and is in fact formally correct in the sense I most often have to use it in, that is Royal Mail addresses), and written language lends itself to greater formality. I had the reverse experience with my [protestant] grandparents in NI on this, where I would in conversation always say 'Derry', while they would equally studiedly say 'Londonderry', again without anyone commenting or attempting to correct or justify. What a peculiar place!