Continuing the discussion from Mapping the music infrastructure in Aotearoa:
My suggestion would be to make both tags 1st class citizens in the interface, hooked to the same underlying discovery mechanisms, and let artists choose for themselves how to identify. If that’s tricky for some reason, feel free to go into detail on why, and I’ll see if I can suggest a workaround.
But also, the best person to ask is not me (not that you did), but the kiwi artists using Mirlo. If possible, as a group, rather than 1 by 1. It might be fun for them all to know they’re not the only flightless bird on the platform.
Good instinct! 
Decolonisation politics is a powder keg in Aotearoa at the moment, and whether the country ought to be called “Aotearoa” or “New Zealand” is one of many increasingly contentious issues. Some people still use them interchangeably, others use one or the other, and get huffy with people using the “wrong” one. As with gendered pronouns, I try to respect people’s self-identification and avoid language policing, although I will challenge any misapprehensions or bigotry I see lurking beneath people’s comments.
Personally, I tend to use “New Zealand” to refer only to the state, the courts, local councils, domestic corporate media, and other institutions set up by European colonists. Also the white bread culture and white supremacist attitudes that go with them. Whether that’s the open bigotry of knuckle-dragging boneheads, or the respectable assimilationism of most of our major current political parties (including Labour BTW).
If I’m talking about the whenua (land), tangata (peoples), or anything else that isn’t itself a product of colonisation - including the country as a totality - I’ll say Aotearoa. But I’m aware that’s contentious even within iwi Māori (indigenous nations). Aotearoa was a name used mainly by iwi in Te Ika a Maui (north island). Iwi in the island I grew up on generally considered themselves to be a separate country, known as Te Wai Pounamu. The history here is complicated further by the fact that the dominant iwi in Te Wai Pounamu came south from Te Ika Maui in the early 17th century, and whether they assimilated the pre-existing populations, or were assimilated by them, depends somewhat on whose oral history you’re listening to.
EDIT 2: I made a major factual mistake, saying “19th century” instead of 17th. I’ve corrected this and linked the claim to a history page on the website of the iwi in question.
EDIT: The historical documents that created our current cultural and institutional arrangements even use different names; He Whakaputanga uses “Nu Tireni”, while Te Tiriti o Waitangi uses “Nu Tirani” (both transliterations of “New Zealand”). Neither uses ‘Aotearoa’, nor ‘New Zealand’, at least not in the untranslated Te Reo Māori versions signed by the rangatira (usually translated as ‘chiefs’, but in this context more like ‘ambassadors’).
Point being, place names are claims, histories, and statements of identity. You’re very wise to tread lightly around issues of geographical nomenclature.
I suspect what would annoy them is if they added the “Aotearoa” tag to their profile and releases, then came back and saw a “New Zealand” tag in its place (or even alongside it) without their say-so. Or vice-versa.