Just was adding "Not now" to a notification dialog in my app today simply because it feels softer. But it's a definite "no", the prompt won't appear again unless you enable notifications yourself later from the settings (hence the "now").

That behavior wouldn't be clear to me as a user unless it were spelled out like you just did. My expectation when I see "Not Now" is that there will be a "Sometime Later". I would recommend changing your language here.

Is there something wrong with "No thanks" ?

Nope, I ended up changing it to that one to avoid the association with nagging prompts.

You could A/B test it. Add a 'not now' and a 'no' button.

I could, but I don't use trackng in my apps aside from some platform/error stats