I think that the original use of the term was as a synonym for anarchist, because anarchism had been outlawed.
Libertarians have to call themselves something - I figure they can keep the word 'libertarian' and old-school libertarians can keep calling themselves anarchists or, if they believe in some sort of government, 'libertarian socialists' (which is also a fun phrase to drop in front of the more ill-educated right-libertarians). The nearest alternative to libertarian in current use is 'anarcho-capitalist' which is problematic for right-libertarians in that most of them believe in some sort of government ('Anarchists who want the police to protect them from their slaves') and problematic for anarchists who think that the capitalist employer/worker relationship is entirely incompatible with any conception of anarchism.
Neo-liberal is already in use for more conventional political outlooks, as other posters have pointed out.
A neo-liberal is just someone who is strongly pro free-trade and possibly some lowered/standardized regulation of business(although not universally, possibly(but not always) formerly or currently associated with center-left(or at least center-left from a US perspective)
Libertarians have to call themselves something - I figure they can keep the word 'libertarian' and old-school libertarians can keep calling themselves anarchists or, if they believe in some sort of government, 'libertarian socialists' (which is also a fun phrase to drop in front of the more ill-educated right-libertarians). The nearest alternative to libertarian in current use is 'anarcho-capitalist' which is problematic for right-libertarians in that most of them believe in some sort of government ('Anarchists who want the police to protect them from their slaves') and problematic for anarchists who think that the capitalist employer/worker relationship is entirely incompatible with any conception of anarchism.
Neo-liberal is already in use for more conventional political outlooks, as other posters have pointed out.