Whatever happened to Junior?

I don’t mean Bush.
As I was watching Brokeback the other day, I was struck by the fact that one of Ennis and Alma’s girls is named Alma Jr. and I got to thinkin’. Do people still do this? Name their kids after themselves. It used to be common. But I was searching through the parents I know with young kids (you know who you are) and I couldn’t come up with a single one who named their son or daughter after themselves. Why has this gone out of fashion? And what was it about in the first place.
Was it egocentric? I want my son to carry my name. Why? What’s so great about you? Have we collectively decided that, nah, there’s nothing so great about us as individuals that we feel we have to stick our name on somebody else. I think people still name their kids in honour of the grandparents, at least for the middle names, but there aren’t a lot of Alma Jr’s around, are they? Especially with girls. I don’t think I’ve ever known a woman who had the same name as her mother. I imagine it was probably more important for fathers to point to their kid and see their rightful heir, name and all, than it was for mothers. I dunno.
From what I’ve read about the 1940s and 1950s, a lot of sons were carrying their fathers’ name without carrying any of their dad’s actual DNA. Was the naming thing part of staking one’s parental claim on the kid, even if he looked just like the milkman. Did the name thing fall away as men become more convinced (sub-consciously) that their boys’ really are their boys and didn’t feel the need to reinforce it publicly with a Jr label?