As far as I know hardly anyone uses the phrase to describe their own politics or ideology, which is telling, so often it is little more than a term of opprobrium.
To me the theory of neoliberalism’s global ascendancy is overblown. I have trouble believing Reaganomics and Thatcherism extended beyond Reagan and Thatcher. The author of the so-called "Washington Consensus", for example, which is often panned as a neoliberal manifesto,
consciously excluded neoliberal ideology like capital account liberalization, monetarism, supply-side economics, or a minimal state.
The background of neoliberalism's supposed rise, I think, is important. It comes at a time when we were witnessing the spectacular collapse of socialist countries on the world stage, the spectacular failure of Keynesian economics, while Thatcher and Reagan were seemingly pulling their countries out of the ruins of statist ideology.
This presented a problem for disaffected socialists after the collapse of the Soviet Union, both ideologically and politically. They could no longer deny that central planning was a failure, and that their popularity was waning. This led critics of the "neoliberalism" of Reagan and Thatcher, and newly disaffected socialists and social democrats like Bill Clinton, Tony Blair, and Gerd Schröder, to re-brand as free market progressives. They tried to push it as a global movement. It's odd; though they were
explicitly critical of the supply-side economics of Reagan and Thatcher, they are somehow considered in the same pantheon as Reagan and Thatcher, with neoliberalism flowing through them.
Personally, I take a different approach. I would call their agenda and the period since Thatcher and Reagan (and perhaps Bush Sr.) "neosocialism", because it better represents the spirit of its architects and reflects their turn away from the Old Left socialism into what Bill Clinton called the New Democrats, or what Blair called New Labour. This political triangulation flows right into "compassionate conservatism" of Bush Jr. and David Cameron. Tony Blair stood in front of the International Socialist Congress in ‘97 and pleaded for a "modernized social democracy", and this modernized social democracy prevails.