Or HaChaim on Exodus 20:7/אור החיים על שמות כ׳:ז׳

1 לא תשא את שם ה׳ אלוקיך לשוא. "Do not utter the name of the Lord your G'd in vain." There is a tendency for people to believe that if they include the name of G'd in an unnecessary oath no harm is done as the very mention of G'd's name is proof that they revere the Lord's name and this adds to His glory. Besides, they argue that as long as the one to whom such an oath is sworn is unaware that the oath is false, how could G'd's name have been desecrated? All the second party knows is that the G'd mentioned in the oath is the G'd of the person swearing it. So what harm is done? G'd replies to such thoughts by saying: לא תשא "do not (even) elevate the name of the Lord your G'd, etc. Even if you have the intention of conferring honour upon My name, do not do it; G'd will not let anyone get away with such use of His name." The reason is that His name was used falsely or needlessly.

2Another reason why using G'd's name to make a lie believable is out of the question is because by doing so the person swearing the oath loses his צלם אלוקים, the image of G'd he has been created with and is known by. Such a person will become known instead as שוא, vain, false, worthless. G'd's name is "truth." Anyone associating that name with a lie, makes the name of G'd "fly away," seeing the person doing so has chosen something vain. An apt translation of this verse would be: "do not remove from yourself the name of the Lord your G'd on account of the pursuit of something that is vain, worthless."

3There is also an allusion here that a Jew should not bandy about the name of G'd giving the impression to all and sundry that he is a true servant of the Lord whereas in reality in his heart he does not serve the Lord. This is why the Torah chose the expression לשוא, i.e. creating a false impression. It is a warning not to pretend to be G'd-fearing. G'd will not allow such people to go unpunished.