I wish there were a clear and easy way to identify these small services owned by PE, who often go out of their way to avoid people finding out.
Usually I find out by noticing symptoms of worsening quality, costs increasing more than I might expect, ramp up in aggressive cross selling of services and subscriptions, shifting to call services that are clearly not local and know nothing of our area, etc.
In some cases I'll get an employee that knows the situation and let's spill the PE sale and then I need to find a new service provider.