Give a dog a bad name is a common phrase in English but few people know the ending!!! See BNC for examples:
Give a dog (so to speak) a bad name, treat him or her accordingly — by having a confrontation or using a suspicious manner — and we are quite likely to trigger a hostile, resentful reaction that confirms our original opinion.
So the ending is interesting but new to me. The shorter version means (as above) that by giving someone a bad name and so by treating them as if they had the "bad name", they will conform to that definition of them. This syndrome is otherwise called a self-fulfilling prophecy.