Sforno on Exodus 20:7/ספורנו על שמות כ׳:ז׳

1לא תשא, invoking the name of G’d when swearing an oath. The word נשא is used in this sense in Kings I 8,31 ונשא בו אלה לאלותו, “when someone utters a curse against another in retaliation, using the curse to make his adversary swear an oath,”

2לשוא, committing perjury thereby; without doubt this oath will backfire on the one uttering it; כי לא ינקה ה' את אשר ישא את שמו לשוא, for having used His holy name to utterly no purpose. Even if the person swearing such an oath had spoken the truth he will not be free from this sin, how much more so if someone used G’d’s name to swear falsely. It is not compatible with G’d’s honour and dignity that man use His Holy name for his own ends. The only time such an oath is permissible, or in some instances even mandatory, is when it is impossible to arrive at the truth by any other means there being no witnesses to the matter under dispute. As far as swearing a false oath, i.e. perjuring oneself is concerned, the Torah has a separate commandment in Leviticus 19,12 spelling this out. ולא תשבעו בשמי לשקר, “and you must not swear an oath in My name when that oath is a lie.”