I would suggest asking IRD directly or get legal advice on this, I can't find a clear answer on Google about this.

You would have to be clear on what the money actually is e.g props up a youtube channel

I would assume so, but if its income then lots of things become expenses so you may work out better off overall.

https://www.govt.nz/browse/tax-benefits-and-finance/tax/income-you-pay-tax-on/

I'd be very surprised if you didn't pay tax on it.  If it's a small amount I think there's some minimum (~500NZD/yr) under which you don't need to do an IR3 tax return, but I can't find the webpage about it.

If you incur costs providing the goods/service/etc that you're getting Patreon money for, you could set yourself up as a business (sole trader or limited company) and only pay tax on the profit.  This requires doing some accounting.  Profit isn't just cash in minus cash out.

The fact that you're asking this question in Geekzone suggests that you do not presently have sufficient knowledge & experience to do your own accounts.  Do you have any friends/relatives who run businesses?  Ask them for advice.