No suitable constructor was found in NUnit Parameterised tests

See the below test fixture:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using NUnit.Framework;

/// <summary>
/// Tests relating to Harry Potter
/// </summary>
[TestFixture("Dumbledore")]
public class HarryPotterTests
{
    public string Name;

    public HarryPotterTests(string personName)
    {
        Name = personName;  
    }

    [Test]
    public void Test()
    {
        Console.WriteLine(Name);
    }
}

What I'm trying to achieve is to see how parameterised test fixtures work. I haven't used them before so this is my first stab at it.

It looks OK to me. Constructor with a string, and passing in a string in the actual test fixture attribute. It compiles. Test simply writes it out to a console window.

The test however fails with this message:

No suitable constructor was found

Am I missing something blindly obvious?

No matter where I put a breakpoint, nothing is hit, so it is failing very early on.