Let us consider the following grid of possibilities (By "the term" I refer to the tetragrammaton; I have tried to exclude possibilities where there appears to be no textual support whatsoever):
||The term originated in the time of Moses
||The term pre-dates Moses
|The term always meant the same thing
|The term was originally generic and became more specific
On this view, the Divine Name is something that was revealed to Moses, was unknown prior to that time, and was always understood as a specific reference to the God of Israel.
In this scenario, either the people were in full, sacrilegious rebellion against God -- their actions were the epitome of taking the name of the Lord in vain -- and their use of the Divine Name to refer to something other than their God was solemn mockery...OR...this started with a genuine, but severely misguided, effort to honor the Lord.
Jeff Benner points out that in the earliest known Hebrew script their pictographic term for "God" was:
The first picture...is an ox head representative of power because of his great strength. The second is a shepherd's staff and is representative of authority as well as a yoke. (The Ancient Hebrew Language and Alphabet pp. 40-41)
In a world where an ox was regularly symbolic of God, and among a people who had been misled by rampant idolatry in Egypt, making a calf might have been seen as a means of honoring God (if so, clearly they were mistaken).
I find it easier to believe Aaron was persuaded to participate by some such analogy than that he went along with willful, belligerent violation of the 2nd & 3rd commandments, but I acknowledge there's insufficient evidence to rule out either possibility--peer pressure is a powerful thing.
On this view the people are using a term that has long been known to refer to Deity, but they were grossly in error (presumably as a result of bad examples in Egypt) in applying the term to a graven image, which is never what the term was meant to signify. In this case the Israelites have fundamentally misunderstood what Moses has taught them about God.
Could the Divine Name have been known before the time of Moses? The plainest reading of Exodus 6:3 would suggest it was not, but it doesn't preclude the use of an equivalent name (though perhaps not in Hebrew) being known to the patriarchs before Abraham. It is noteworthy that the tetragrammaton does appear in the book of Genesis, prior to the lifetime of Moses. This could be because:
- When Moses wrote Genesis he included the Divine Name because he himself knew it, even if the people he was writing about did not
- The patriarchs hade an equivalent term, and Moses translated it using the Divine Name
- Exodus 6:3 has been misunderstood, and Abraham et al did know the tetragrammaton root, even if they did not understand its significance to the extent Moses did
On this view the tetragrammaton was revealed to Moses but, at least in common usage, was understood the way the word "god" (lower-case) is often used in contemporary English. A comparable example would be the Hebrew Elohim, which as a title properly refers to the God introduced in the very first verse of the Bible, but was also used more generically to refer sometimes to His representatives, and sometimes to false gods.
The children of Israel may have misunderstood what Moses was trying to teach them about God (what a shock!), and it was over time that they came to recognize that the Divine Name should be used as a specific reference to the God they worshipped and not to anything else.
Note that this option is difficult to reconcile with the revelations Moses received in Exodus 3 & 6, unless we conclude that later editors of the Torah wrote back into Moses' words the words they used to refer to Deity, even if that wasn't the way Moses did. To me this appears to be a stretch, especially because the Torah is saturated with usage of the tetragrammaton.
On this view, the Divine Name was used in Hebrew, prior to Moses, as a generic term related to God or gods, and the idol was thus referred to with this name not as a means of adding insult to injury in mocking God, but because they saw the idol as a deity and that was a plausible means of referring to a deity. Over time, Israel came to apply the term specifically to the Lord and only the Lord (see Leviticus 24:16 as an example where this new, technical usage, would be taught & enforced).
In this case, the Israelites may not have been breaking the 3rd commandment, though they were certainly breaking the 2nd.
The possibility of the Divine Name--or something related to it--predating Moses, and the implications of Exodus 6:3, would be the same here as they were for option B.
Under option A, the Israelites are not necessarily using the tetragrammaton to refer to the idol, but as a misguided attempt to honor & refer to the Lord.
Under option B, the term is being applied erroneously to the idol.
Under options C or D, the term wasn't originally unique to the God of Israel--it was a generic Hebrew word--that was later consecrated as the respectful term for the God of Israel. In these cases the term is being applied to the idol.
I find option A the most plausible, though I do not believe there is sufficient textual or historical evidence to entirely rule out competing possibilities. If option A is correct, Israel may never have used the tetragrammaton to refer to anyone or anything other than the God of Israel. On the other options presented, Israel did, as part of a violation of the 2nd commandment (and possibly the 3rd) exhibit the unusual behavior of using the tetragrammaton to refer to a false god.