Simple Math Quiz Game
Even though this is a fairly short program, resist the temptation to do everything in the Program class of your console app. Whenever I start a new console app, the first thing I do is create a Runner class with an Execute() method and call that from the Main() of Program.



Using goto is IMHO incredibly rare in a C#/.NET program. Make this code block a method and call it.



Whenever you start copy-pasting code, it's a sign you're doing something wrong.

switch (responseIndex)
{
    case 1:
        Console.WriteLine("Great!");
        Console.WriteLine("Your score: " + score);
        break;
    case 2:
        Console.WriteLine("You nailed it!");
        Console.WriteLine("Your score: " + score);
        break;
    case 3:
        Console.WriteLine("You're correct!");
        Console.WriteLine("Your score: " + score);
        break;
    default:
        Console.WriteLine("Good Job " + userName + ", Keep it up!");
        Console.WriteLine("Your score: " + score);
        break;
}


Clearly Console.WriteLine("Your score: " + score); should be in a method of its own, and the other line you be as well, with its message the parameter for that method, e.g.

private void ReportResult(string message, int score)
{
    Console.WriteLine(message);
    Console.WriteLine("Your score: " + score);
}


You could even write the second line as Console.WriteLine("Your score: {0}", score); or Console.WriteLine($"Your score: {score}");. While a small amount of string concatenation isn't a performance killer, newer versions of C# offer nicer and more readable ways to format strings.



int Answer: "Answer" should be camelCase.



Considering that you calculate int correctAnswer = num01 * num02;, why then do you do if (Answer == num01 * num02) next? Use correctAnswer.



Even though the current code is fairly short, I'd still move the code in the if and the code in the else block to a method of their own (e.g. "ReportSuccess" and "ReportFailure"). This will make your code easier to follow and splits up the logic into smaller chunks.