Your wrong about this. The actual term for this (as I mentioned above) is psychological egoism. This topic has been publicly debated for a very long time. You can look at the history of the debate between egoism and utilitarianism (and the further debate about whether there’s a meaningful difference between those two ideas) if you want to learn about it.

People have debated for a very long time whether a person who derives satisfaction from benefitting others is truely motivated by the benefit of others, or simply the benefit of themselves by way of that satisfaction. A narcissist is a completely different thing. They would not derive satisfaction from benefitting others, for reasons such as their narcissistic lack of empathy.