Every fourth year is a leap year, except multiples of 100 unless it's a multiple of 400. That was the core of the change to the calendar which gave it a new name.
It almost lasted an entire cycle. Introduced in 1582, it was functionally replaced in 1972 by a system involving leap seconds, which sound pretty minor but are sort of weird for calendars because you can't project them into the future more than six months. Now no calendar exists with total accuracy without updates, and preferably an internet connection. That's a bit beyond the old system's capability.
There's something oddly sad about a system being designed so that errors wouldn't accumulate over millennia, and having it replaced without even being fully used first. These things are built for extreme longevity, but never get used for an extremely long time.
I appreciate social permaculture, the attempts to make our institutions last beyond us. Because (I hate to break it to you) with billions of humans, all of us are replaceable. We have to be – we all die. So if we're replaceable, why not build things that endure when we cannot?
Not just family, of course. But since it is the obvious suggestion, I will take the time to note: people do not take family names or traditions very seriously anymore. At least this averts the strange age-old American customs of family feuding, but there aren't dynasties anymore. I strongly suspect building inter-generational wealth will be made more difficult too – business uncertainty combined with inheritance taxes have been making it more difficult and both seem likely to become bigger obstacles in the future. So while your children will outlive you, an institution probably will not.
Perhaps the strength of an institution is to keep it's name past when it keeps its influence. The Catholic Church could no longer make any claims to stop the tide of leap seconds. But we didn't change the name. Perhaps that honor is all that we can leave behind. But I'd like to think we can build our values into a system as well. I'd certainly like to give it a try.