I know you should capitalize people's names, but should you really capitalize God if it is the name of nothing?

Depends in what context you capitalize. If your referring to God directly because of your religion (any religion) and you believe in him then yes you should. But if your referring to god in a phrase or a god you don't believe in you don't have to capitalize. Also God is like a name so in proper English "God" would be capitalized because it refers with other religions.