'Do you not know that a man is not dead while his name is still spoken?' -Sir Pratchett

Given how much weight most folks put in defining themselves through other people...

A lot of people care about their legacy.

And sometimes the legacy is just that the world is a better place thanks to their efforts, and has not much to do with having your name all over the place.

You might care about your legacy while you're alive, but after you're dead, there is no you, so it's not possible for you to care about your legacy after you're dead.

But only before they die.

A lot of universities end up renaming buildings after later rounds of donors, so even getting your name up on the building isn't a guarantee.