Help with naming my daughter

As the title says, with my wife we are expecting a girl and we are thinking about names. I have a South American upbringing where we have 2 surnames (father surname + mother surname) but my partner also acknowledges that in the dutch culture having 2 surnames is kind of weird, even tho since last year, you are allowed to have 2 surnames now in the Netherlands.

Does anyone know how this new ruling for 2 surnames work? For example in Chile where I come from, you legal name is your name + 2 surnames, but oftenly people just use their name + their first surname, except if it is strictly necessary (such as a legal document etc) Would it be the same in the NL or would they be strict as to say that you MUST always use your 2 surnames even if you're ordering from bol.com ?

TIA

Edit: My partner is dutch, so the 2 surnames would be her surname + my latin surname if that's the case.