Considering that a name is much more than just a name in the cultural mileau of Matthew's gospel, I believe that we are talking about more that avoiding thoughtless usage of the word "God" or "Jesus". Since a name is the representation of the person, when we speak and/or teach about God or Jesus our words should reflect Him as He truly is (in so far as we are capable of knowing God. We can never know God wholly, but we can know Him truly). To speak or teach in a manner that would lead someone to believe God to be someone He is not would be profaning His name.
We who bear the name "Christian" should live up to, with God's help, our name. Our lives should be more and more a reflection of Him whose name we bear so that Christian is a name that is representative of us. Not because we have to, not because we are afraid of bringing dishonor to our Christian family, but because we love Jesus and want to be just like Him when we grow up. This attitude, I think hallows His name.