Let’s say I become a citizen of a country that doesn’t allow dual citizenship. During naturalization, new country B tells me I have to renounce citizenship from old country A.
Does that have any effects back in country A? How would country A know? Would country A even care if they found out?
No, other way around. Most countries won’t even allow you to renounce if you don’t have another citizenship.
The US also charges $10,000 dollars to accept your renunciation. The US is one of the few countries that taxes its citizens in foreign countries so there’s a big incentive to renounce when you get citizenship in a better place. There is a substantial tax deduction for the first ~150K you earn in another country, as long as you spend less than 10 days in America or traveling and pay taxes in that country, as long as that country has such an agreement with the US.
It’s $2350 to renounce, not $10k.