I'm UK, French and NZ. Within Europe I stick to my UK passport on the booking, even though within the rest of Europe (and except Ireland and Gibraltar) I present my French passport at the EU/EEA/CH Border. I know I should switch the passport over in BA but no-one seems terribly bothered by that so nor am I. USA and Canada are linked to my UK passport anyway, so I only flip to NZ for Australia and NZ, and France for a tiny number of places where it's just easier or cheaper (e.g. Lebanon and previously Russia).