Yeah, was about to point out the same thing. I’m a little surprised - it’s one thing for a global tech giant to build a service that competes with yours, but it’s another to use exactly the same name. Is that actually allowed?
The only form of trading name protection is a trademark. So if neighbourly.co.nz wanted to expand into new markets, their next move would be a WIPO filing for their trademark - but you can't just register a trademark in a country and not trade under it there, it's easily challenged.
And after having searched IPONZ's website, it appears that there's not even a registered trademark in NZ for neighbourly - so if Google were to start trading in NZ using "neighbourly", neighbourly.co.nz would have to rely on the passing off provisions of the Fair Trading Act and be able to produce evidence that Google had caused them loss by confusing their customers.
TL;DR - trademarks are important.
As an aside, based on spelling (-our vs. -or) I presume this Google product comes from a non-American market.