The JASA manuscript template contains the Keywords section to insert 3-6 keywords. Is it appropriate to insert there the proposed method name as one of the Keywords?
If yes, should I use method's acronym (well-sounded but not self-explanatory, a 5 letters-long word) or the full name (4 words)?
If the method is important to your work (e.g. if the method has a "blind spot" so the results might have a loophole) then yes, include it as a keyword.
As for whether to use the full name or the acronym, either is fine. When the template says "3-6 keywords", chances are very good that each group of words is one keyword. For example, "United States" would be one keyword, even though it's two English words.
