"A good name is rather to be chosen than great riches."

This statement means that you want people to remember you by your name not by, "Oh he's the kid who was mean wasn't he?" You want people to say, "Oh Peter, yeah I remember him, he was really nice." We don't want people to see as the person who only care about materials and not the people that surrounded them. You want to be remember for your personality and how you were as a person, noy for the cool stuff you had. At the end of the days those things don't matter, we will all end up dying, the only difference will be the legacy you left in the world. We want our legacy to change the world for the better and for that reason we should care more about our name than the stuff we may have.