I use the holy name of "God" for that reason! But if I say, "Oh my God," I cross myself to make it clear I mean it as a prayer and just have no other words (accident, whatever).
If someone uses the Holy Name of Jesus in vain, which happens just far too often, I'll try to holy it up for them (cross myself, bow my head and cross myself, or if it's particularly bad, an Act of Contrition, but since you can't really say that for someone else, I start it out loud and leave the offending party after "having offended thee"). I fear most times you can't holy up what has been said, and you just have to leave. I don't go to live sporting events anymore because the Holy Name is used as an expletive after a bad plays.
I don't mind "Touchdown Jesus" because it's an actual mural, but my husband detests it. Not because he hates the Irish (which, true, he's not a fan), but because he feels the mural is offensive, and asks if we are giving our Lord the credit for other teams' touchdowns too. I'd always thought of it as like "Deo Gratias", but things get ingrained in your head, and he has a point. :/