what do you call a person who has chosen not to have children?

The person can be said to be childless:

COBUILD Advanced British English Dictionary
adjective
Someone who is childless has no children

However, this word is too vague to fit your request: it covers both involuntary and voluntary childlessness. As that Wikipedia article indicates, one adjective that is used to describe the latter state is child-free or childfree. I don't personally care for the term; to me it has the same "trying to force a positive connotation" vibe as "80 years young." I have no idea if many other people share my prejudices, but Wikipedia says the adjective was coined relatively recently (the late 20th century) and many publications still put it in quotation marks when they mention it (example: 5 Things ‘Childfree’ People Want You To Know–Huffington Post).

An acronym which is entering the lexicon is "DINK" (dual income no kids), or "DINKY" (dual income no kids yet). The two alternatives mean the same in practise.

The "dual income" part means that both people have a job, so the meaning is slightly more complex than just "not having any children".

It may be that DINK is more commonly used as a noun and DINKY as an adjective, since that mirrors many other words in English that form an adjective with the addition of a "Y". Personally I have encountered the "DINKY" form more often.

It may be a little informal for your needs (you haven't specified the context in which you want to use it so I don't know).

There is no stigma attached, and may often be self-applied, eg "Since we're a DINKY couple we can, perhaps paradoxically, afford a bigger house."

https://en.wikipedia.org/wiki/DINK_(acronym)

Antinatalist

Anti-natalism is a philosophical position that assigns a negative value to birth or claims that one should not reproduce.

Other philosophies that could lead one into such position: (ethical)

• Negative utilitarianism, aims to reduce or avoid negative well-being
• Existential nihilism, posits that life has no intrinsic meaning or value

One can also reason that this preserves more freedom and resources for the adult (economical)