Thank you cosmoskey, you can even join the map and joinToString together

I guess the type of n should be changed to long to fulfill 1  ≤  n  ≤  10000000000. Since int can only hold values up to 2147483647.
Also method names starting with an uppercase letter is unusual. I propose to change it to the following for Java

public class Line {
    public static String whoIsNext(String[] names, long n) {
        // Your code is here...
    }
}

Another point is that you actually access static methods in Java without an instance of Line. You would also have to change the type of n if you apply my suggestion from above.

...
public class ListTests {
    @Test
    public void test1() {
        String[] names = new String[] { "Sheldon", "Leonard", "Penny", "Rajesh", "Howard" };
        long n = 1L;  
        assertEquals("Sheldon", Line.whoIsNext(names, n));
    }
...