Before our son was born, my wife and I talked about all the different names we could give to him. Some of them were funny. Some were unusual. Some were traditional. We settled on Samuel, and now we can't imagine him with any other name. His name and his identity are connected. He is Sam. Sam he is.
God takes His own name very seriously. Throughout Scripture, He makes a huge deal about it. He is connected to His name, especially Yaweh, in a sense that goes beyond the connection we have to our own names. It is His identity, His reputation, and it carries His power.
So this command is a warning: If you disrespect God's name, you disrespect Him. How would you do that? You could borrow its power for lying ("I swear by God's name I didn't cheat on the test!") or -- in the ancient world, especially -- for certain ungodly spells or rituals.
But the most common way to misuse His name now is to use it as if it doesn't matter, at all, by cussing with it, joking with it, or "damning" people or things with it (even if you don't really mean it). The third commandment tells us that God takes that personally.
Think: Have you noticed yourself or other Christians using God's or Jesus' name disrespectfully? Why do you think so many of us seem to be okay with that?
Pray: Ask God to help you to never use His name inappropriately or disrespectfully.
Do: Notice how many times you hear people use God's or Jesus' names for swearing in the next few days.