Create a class TestWithParameters.

This class keeps the data together that are needed for creating a runner for a single data set of a parameterized test. This makes it also clear, that the computation of the name is not the responsibility of the runner but of the Parameterized class.
Make the inner class TestClassRunnerForParameters static.

The class can new be used without an Parameterized instance. It is now self-contained.
Extract BlockJUnit4ClassRunnerWithParameters.

Separate the class from the Parameterized runner. Makes it clear, that it is designed for reuse.
Use a ParametersRunnerFactory for creating the test for a set of parameters.

There's now an explicit component for creating the runner of a single set of parameters. IMHO this is a better extension point than overriding a method.