I don't see how you can smash the "whack-a-mole" machine because I don't see there as being one. People don't identify as "neoliberal", people who are anti-neoliberal identify other people as neoliberal.
For instance, ISIS has a "whack-a-mole" machine for it's ideology in Syria, and people identify with ISIS when they commit muslim extremist activities. All issues aside with leveling Syria into a parking lot (let's say we instead just transport it to another dimension so we don't go down that discussion path), even with Raqqa gone and all ISIS strongholds gone, it's still an ideology that people can identify to and will still have people pledging allegiance to it. Same with Anonymous, it's an idea that hacktivists can attach to, with no real "whack-a-mole machine" that can stop it.
However, in this case, we aren't even dealing with something that has a name that people identify with. Politicians don't pass "neoliberal" laws and claim it a victory for neoliberalism. What one person calls neoliberal someone might call neoconservative, and other might call crypto-facist, or another might call anti-progressive.
So I'm guessing the idea is to put a name to a bunch of people who fall into your respective category for neoliberal, and then get people to rally against the concept. Then people will say they aren't neoliberals, because they never identified with it in the past nor ever even heard of it.
It sounds like the very beginnings of a neo-McCarthyism. You start by labeling people who really are as you classify (contrary to what McCarthy was doing, hence "neo"), then everyone else changes the definition ever so slightly and then everyone just starts finger pointing at each other until we've accomplished nothing.
I don't see the benefit whatsoever.