How do you know that there is a God, and that God is Krishna?
There's only one Supreme Being, but He has many names. Krishna & Rama mean "He who is the most attractive" and "He who gives the highest pleasure." Anyone who accepts God will accept that He is the most attractive and that a relationship with Him gives the highest pleasure.
Krishna Himself says that he is the source of everything in Bhagavad-gita 10:8 — "I am the source of all spiritual and material worlds. Everything emanates from Me. The wise who perfectly know this engage in My devotional service and worship Me with all their hearts." But He also is selective about who He reveals Himself to:
"I am never manifest to the foolish and unintelligent. For them I am covered by My internal potency, and therefore they do not know that I am unborn and infallible." 7:25
We see that in the material world everything has a cause. Nothing comes from nothing. With a little intelligence, one can see that there's intelligence behind everything...so why should we consider that this vast material world, with so many complex arrangements, came about by chance? It really doesn't make sense. So if there is a God, and you accept His existence then you should also consider that He is one, and has many names, and Krishna is one of them.
Also, if doubting persons try to chant Krishna's name with faith, they will also come to know that Krishna is God; on the absolute platform, God and His name are the same.