I had understood it to mean, like, making an oath (“I swear to God…” or the whole hand-on-a-Bible swearing) and not following through, or making it lightly.

Jesus had a whole thing about it, saying that not only should you not make an oath in God’s name lightly, but that you shouldn’t at all (implying it shouldn’t be necessary, if you’re already an honest person). “Let your yes be yes, and your no be no.”

Which, honestly, makes way more sense than some nonsense about not saying their names.