Since my first name is Stanford (I go by Stan), which is an old family surname, at my age (over 70) I admit to finding some of the comments rather humorous. Each of us are given our birth names without our having any say in it, and much of the time we grow into that name, and over time can find that the name fits us. In my case, I have often (even inadvertently) been one to help others to cross over a barrier (like the stone in a ford of a river), whether in school, or work or a life crisis.
Stanford is too tied to the university and this is my only link with it.It has a sort of WASP-snobbish, upper class and preppy vibe (e.g. like a possible character in 'Gossip Girl').
Because of the university, I could never name my son this. Ew. With that being said, I have seen it used as a given name through a family friend's classmate. It's rather unusual.