is there a name for the widely-held belief/feeling/intuition that some of our ego or consciousness is inside of your children, that if you have children you're continuing your "bloodline" and that your descendants are part of a chain of beings that add up to one whole?

It's clearly implicit in the thought of most people who've procreated throughout all of history. expressions like "genetic dead-end" are used in a modern understanding for people who fail to procreate, and I'm pretty sure I've read this kind of thought being called "genetic immortality" before but when I look that up I find hardly anything. It's surely a big enough topic that whatever it's called, it definitely has a wikipedia page all on its own, but I can't find it. I know there's a lot of crossover with this belief/feeling and more developed theological concepts like reincarnation - I know that European pagans believed they can only reincarnate as one of their descendants. but I want to know what the more basic, intuitive sense is called when a father sacrifices himself for his children.