You shall not swear falsely

(ז) לֹ֥א תִשָּׂ֛א אֶת־שֵֽׁם־יְהוָ֥ה אֱלֹהֶ֖יךָ לַשָּׁ֑וְא כִּ֣י לֹ֤א יְנַקֶּה֙ יְהוָ֔ה אֵ֛ת אֲשֶׁר־יִשָּׂ֥א אֶת־שְׁמ֖וֹ לַשָּֽׁוְא׃ (פ)

(7) You shall not swear falsely by the name of the Eternal your God; for the Eternal will not clear one who swears falsely by His name.

Friedman, Richard Elliott. Commentary on the Torah (S.1183). HarperOne.
You shall not bring up the name of YHWH, your God, for a falsehood, because YHWH will not make one innocent who will bring up His name for a falsehood.
כי אתא רב דימי אמר רבי יוחנן אוכל ולא אוכל שקר ואזהרתיה מהכא (ויקרא יט, יב) לא תשבעו בשמי לשקר אכלתי ולא אכלתי שוא ואזהרתיה מהכא (שמות כ, ו) לא תשא את שם ה' אלהיך לשוא
§ When Rav Dimi came from Eretz Yisrael, he reported that Rabbi Yoḥanan says: If one takes an oath, saying: I will eat, or: I will not eat, relating to the future, and does not fulfill it, it is a false oath. And its prohibition in the Torah is from here: “And you shall not take an oath by My name falsely, so that you profane the name of your God; I am the Lord” (Leviticus 19:12). If one takes an oath, saying: I ate, or: I did not eat, relating to past actions, and it is a lie, it is an oath taken in vain, and its prohibition in the Torah is from here: “You shall not take the name of the Lord your God in vain; for the Lord will not absolve of guilt he that takes His name in vain” (Exodus 20:7).
עוד ירצה כי באמצעות שבועת שוא הוא נושא מעליו שם ה' הנקרא עליו ומתלבש בבחינת הרע המתיחסת בשם שוא כי שם ה' אמת והמזכירו בשקר פורח ממנו בחינת השם לסיבת בוחרו בשוא, וזה הוא שיעור הכתוב לא תשא מעליך שם ה' אלהיך לסיבת שוא, ואמר כי לא ינקה ה' לעושי כן:

Another reason why using God'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 God he has been created with and is known by. Such a person will become known instead as שוא, vain, false, worthless. God's name is "truth." Anyone associating that name with a lie, makes the name of God "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 God on account of the pursuit of something that is vain, worthless."

שלא לשבע לשוא - שלא נשבע לבטלה, שנאמר (שמות כ ז) לא תשא את שם ה' אלהיך לשוא, וענין הבטלה בארבעה צדדין, כגון (שבועות כט, א) שנשבע על דבר ידוע שאינו כן, כגון על עמוד של שיש שהוא של זהב, וכן כל כיוצא בזה, הצד השני, כגון [ירושלמי שבועות פ"ג ה"ח] שנשבע על הידוע שהוא כן, כגון על האבן שהוא אבן ועל העץ שהוא עץ, וכל כיוצא בו, הצד השלישי, שנשבע לבטל מצוה זו, או מצות שחיבנו השם ברוך הוא, שגם זה לבטלה לגמרי, הוא שאין בידו לשבע על מה שכבר חיבו האל, וכמי שנשבע בדבר ידוע שאינו כן הוא. הצד הרביעי, שנשבע לעשות דבר שאין בו כח לעשותו, כגון (שבועות כה א) שלא יישן שלשה ימים רצופים, או שלא יאכל שבעה ימים רצופים, וכן כל כיוצא בזה.
To not swear in vain: That we not swear pointlessly, as it is stated (Exodus 20:7), "You shall not take the name of the Lord, your God, in vain." And the notion of pointlessness has four angles: [The first is,] for example (Shevuot 29a), that he swears about something known [to be true] that it is not so, like swearing about a pillar of marble that it is a pillar of gold. And so [too], anything like this. The second angle is, for example [Talmud Yerushalmi Shevuot 3:8], that he swears about what is known to be so, like about a stone that it is a stone and about a tree that it is a tree, and all that is like this. The third angle is that he swears to negate this commandment or the commandments that God, blessed be He, commanded us; as this is also completely pointless, since it is not in his hand to swear [to negate] that which God has already obligated him - and it is like the one who swears about something known that it is not so. The fourth angle is that he swears to do something that he does not have the power to do; for example (Shevuot 25a) that he will not sleep for three consecutive days, or that he will not eat for seven consecutive days. And so [too], anything like this.
Friedman, Richard Elliott. Commentary on the Torah (S.1183-1184). HarperOne.

Ex 20:7. bring up His name for a falsehood. (Traditionally translated “take His name in vain.”) This does not mean that one cannot say the divine name in an exclamation—much less does it mean saying the words “God” or “Lord” in an exclamation. It refers to falsehood. The term refers to a false report (Exod 23:1) and a false witness (Deut 5:17; which corresponds to the term “lying witness” here in Exod 20:13). This commandment means that one cannot make an oath in God’s name and not fulfill it. To appreciate the seriousness of this commandment, note the case of Joshua, who is deceived by the Gibeonites into making an oath of nonaggression. When Joshua learns that the Gibeonites are among the Canaanite residents whom he was commanded by God to destroy, he lets them live, disobeying a direct command from God rather than violate one of the Ten Commandments (Joshua 9). And note the case of Jephthah, who makes an oath to sacrifice the first thing to come out of his gate, which turns out to be his daughter. He sacrifices her rather than violate this commandment (Judges 11). (It is not reckoned legally as murder. Human sacrifice is forbidden, but it is legally distinguished from murder, which involves malice.) As horrible as this is (especially in light of the Aqedah), it conveys the seriousness of this commandment and of the principle that the Ten Commandments outweigh other laws.
לֹ֥א תִשָּׂ֛א אֶת־שֵֽׁם־יְהוָ֥ה אֱלֹהֶ֖יךָ לַשָּׁ֑וְא כִּ֣י לֹ֤א יְנַקֶּה֙ יְהוָ֔ה אֵ֛ת אֲשֶׁר־יִשָּׂ֥א אֶת־שְׁמ֖וֹ לַשָּֽׁוְא׃ (פ)
Thou shalt not take the name of the Lord thy God in vain; for the Lord will not hold him guiltless that takes his name in vain.
הָא גוּפָא קַשְׁיָא: אָמְרַתְּ הַמַּבְדִּיל בַּתְּפִלָּה מְשׁוּבָּח יוֹתֵר מִמִּי שֶׁיַּבְדִּיל עַל הַכּוֹס, אַלְמָא תְּפִלָּה לְחוּדַהּ סַגִּי. וַהֲדַר תָּנֵי אִם הִבְדִּיל בְּזוֹ וּבָזוֹ — יָנוּחוּ לוֹ בְּרָכוֹת עַל רֹאשׁוֹ. וְכֵיוָן דְּנָפֵיק לֵיהּ בַּחֲדָא — אִפְּטַר, וְהָוְיָא בְּרָכָה שֶׁאֵינָהּ צְרִיכָה, וְאָמַר רַב וְאִיתֵּימָא רֵישׁ לָקִישׁ, וְאָמְרִי לַהּ רַבִּי יוֹחָנָן וְרֵישׁ לָקִישׁ דְּאָמְרִי תַּרְוַיְיהוּ: כׇּל הַמְבָרֵךְ בְּרָכָה שֶׁאֵינָהּ צְרִיכָה — עוֹבֵר מִשּׁוּם ״לֹא תִשָּׂא״!

This baraita is apparently self-contradictory. On the one hand, you said that one who recites havdala in the Amida prayer is more praiseworthy than one who recites havdala over the cup of wine, indicating that reciting havdala in the Amida prayer alone is sufficient. And then it is taught: If one recited havdala in this, the Amida prayer, and that, over the cup of wine, may blessings rest upon his head. And since he fulfilled his obligation to recite havdala with one, he is exempt, and the additional recitation of havdala over the cup of wine is an unnecessary blessing. And Rav, and some say Reish Lakish, and still others say Rabbi Yoḥanan and Reish Lakish both said: Anyone who recites an unnecessary blessing violates the biblical prohibition: “Do not take the name of the Lord your God in vain” (Exodus 20:7).

לא תשא את שם מאחר שלא ראית שום תמונה אין יכולת לישבע רק בשמו ואעפ״‎כ לא תשא, לשוא כי לא ינקה אבל הגוזל והחומס יכול לנקות עצמו, זה ניתן להשבון וזה לא ניתן להשבון.

לא תשא את שם, “do not utter the sacred name, etc.” Seeing that you have not ever seen a visual image of God, you can obviously not utter an oath by invoking someone else as a deity. Even so, you must not even swear an oath in His name unless there is an absolute necessity to do so, as God does not allow His sacred name to be used for profane reasons, or for secular purposes. This is one sin which will not be subject to being wiped out even by repentance, i.e. כי לא ינקה, “He will not consider such a person as being free from guilt.”

לשוא לחנם כתרגומו. אל תרגיל עצמך לישא את שמו בחנם אפי׳‎ באמת שמתוך הרגילות תבא לישא את שמו לשקר ואז לא תנקה. כי לא ינקה ה׳‎ את אשר ישא את שמו לשוא ולשקר.

לשוא, “in vain.” Do not make a habit of prefacing any parts of your speech by invoking the name of God (unless as a pseudonym), even if what you say is the truth. The very habit of uttering God’s name on too many occasions will lead you to do so when it is a blasphemy, or an outright lie. If that were to happen it would result in an unforgivable sin, i.e. כי לא ינקה.

לא תשא וגו' (שמות כ, ז). הטעם, שאפילו מלך בשר ודם מקפיד כשישבעו בשמו בחנם, קל וחומר ליוצר כל. וצריכין אנחנו לידע ולקבוע בנפשותינו ולחזק האמונה בלבותינו כי האל ברוך הוא אשר בשמים ממעל חי וקים לעד אין קיום כקיומו, וראוי ומחויב עלינו בזכרנו שמו הגדול על מעשינו ועל דבורינו לזוכרו באימה ביראה ברתת ובזיע. ולא כהמהתלים ומדברים בדבר קל כמו בדברים ההוים ונפסדים ואינם נשארים בקיומם כמונו אנחנו בני אדם, ושאר דברי העולם השפל, על כן ראוי לקבוע הענין הזה בלבינו ולהיות יראתו על פנינו, לבל נזכיר שמו הקדוש לבטלה, וכל שכן לשקר שאז הוא משקר באמונתו רחמנא ליצלן:

לא תשא. Even a king of flesh and blood insists on not lending his good name to something criminal or dishonourable. How much more so is the Creator of the entire universe entitled to have His Holy Name respected! We must remember that the existence of the Lord our God, i.e. His eternal existence, is not comparable to any other existence in this universe. This awareness must be reflected whenever we utter His Name, something that must be accompanied by feelings of awe and reverence. One does not use His Holy Name in light-hearted conversation. It is not appropriate to bring God's Name into conversations which deal with transient matters. Needless to say that it is even less appropriate to associate His name with lies and cheating.