Perception is power.
Those who control perception has the power.
Names are what identifies those things that are perceived.
A person who hears a word will associate it with the object they perceive as the name.
Something that uses the same word will be a challenger to the original name.
The owner of the original name will call the challenger illegitimate.
Money is the standard medium for exchange in a given economy.
Money is perceived to be measured by "Dollars" in the United States.
"Dollars" are perceived to be "Federal Reserve Notes" in the United States.
Federal Reserve Notes are percieved to be owned by the United States Government.
The United States Government has been perceived to have permitted the Federal Reserve Bank the right to handle the word "Dollar."
The United States Government has not been perceived to allow anyone else to compete with it.
The United States Government calls the competition's "Dollar" illegitimate.
Because the government is perceived to own the concept of the "Dollar," the government's claim is perceived to be legitimate.
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Now, from that stream of consciousness, I hope you pick up something of my point. I'll admit, I'm not a logic expert, so I probably glossed over some logical details, but I'm sure my point is clear.
As long as the term "Dollar" is tied to the "Liberty Dollar," it has to overcome the perception that "Dollar=FRN," and that "Liberty Dollar=Counterfeit FRN."
As such, you'd be fighting an uphill battle. Were you to just reject the use of the word "Dollar," however, and either coin a new word, or just use the word "Liberty," or something similarly different, you can own the new measure for money, completely divorcing it from the Federal Reserve Bank, and giving it a chance to be a completely independent form of currency, which gives it its own validity.
Of course, it never hurts to have a website dedicated to offering the current exchange rate for the medium, whatever it be called.