Google and Bing searches for "creo" give the PTC product as their first result. IANAL, but PTC could make the case that you are diluting their brand name by using it for your software, or worse, trying the phish their customers.

Is using part of someone else's name a violation of trademark laws? I'm genuinely curious!

I chose Creo because it means "to create" in Latin (I'm a sucker for Latin names), with docs obviously being short for documents.

I'd argue that Creo is just a generic word, it's not like the name is Leicadocs where that word is very firmly tied to a single company.

Potentially. If you stay away from mentioning or advertising anything related to their line of work (CAD software?) they'll have less of a claim of infringement. Also, trademark the name in NZ, if you haven't already. IANAL, YMMV, etc...