What is the equivalent of TestName rule in JUnit 5?

Declare a parameter of type TestInfo in your test method and JUnit will automatically supply an instance of that for the method:

@Test
void getTestInfo(TestInfo testInfo) { // Automatically injected
    System.out.println(testInfo.getDisplayName());
    System.out.println(testInfo.getTestMethod());
    System.out.println(testInfo.getTestClass());
    System.out.println(testInfo.getTags());
}

You can get test method name (and more) from the TestInfo instance as shown above.