This is kind of my family. My brother and I have not fathered any children, he's a step dad, with no intention to have any of his own, I'm happily in a childfree relationship.
The only (sort of) exception is that my eldest brother (of three), had four kids.... All girls.
So our biological lineage will continue, but our family name ends here, since once my niece's get married, our family name will be dead.
The closest continuance of our family name is through my one male cousin on my dad's side. I don't keep in touch with him enough to know if he has kids or he's planning to have kids, or to even be informed as to whether or not those children would be boys or girls, etc.
After that, you would have to go back about 3 generations to find someone of the same lineage that's actually continuing the family name. Second or third cousins... I believe. I'm unaware if my grandfather had any siblings, or cousins... So that part of my family tree is a complete unknown.
For my brother, he wasn't in a stable relationship long enough to get married and have kids (though, he's on his second marriage, the first did not last very long.... It's a long story as to why)... And since his second wife (his current wife) already had children from a previous marriage, he has no interest. For me, I never cared either way, and stuck to the philosophy of "I'll let my wife decide". My current, and longest, relationship, under which we've been together for nearly a decade now, is with a beautiful woman who has been very childfree for a long time, and I support her in that. I also wouldn't be able to financially support children, which is why I kept waiting for marriage before kids. I at least wanted the illusion that someone was going to stick around before making that commitment.
My oldest brother got married pretty young and to his credit, they're still together. I'm mostly estranged from him, but I'm aware of some of the details of his life. His children are at the age where they can start having kids of their own now (which should give some indication of how old I am... I'm "great uncle" age). I don't have any pressure to have kids at this point because my SO doesn't want them, my breeder brother is estranged, my father is dead, and I'm estranged from my mom. The only time I even hear about kids is either from my sister-in-law taking about her (now post-teen) children, and from my SO's family, who we see online only a few times a year at most.
I don't feel like I'm missing out.