If I understand well, you want to use a list of string dynamically created to define the value of a string.

Here is the class I use:

public class MyClass
{
    private List<string> myNames;

    public MyClass()
    {
        myNames = new List<string> { "jack", "pam", "phil", "suzan" };
    }

    [Browsable(false)]
    public List<string> Names
    {
        get { return myNames; }
    }

    [TypeConverter(typeof(MyConverter))]
    public string SelectedName { get; set; }
}

And here is the type converter:

public class MyConverter : TypeConverter
{
    public override bool GetStandardValuesSupported(ITypeDescriptorContext context)
    {
        return true;
    }

    public override StandardValuesCollection GetStandardValues(ITypeDescriptorContext context)
    {
        // you need to get the list of values from somewhere
        // in this sample, I get it from the MyClass itself
        var myClass = context.Instance as MyClass;
        if (myClass != null)
            return new StandardValuesCollection(myClass.Names);

        return base.GetStandardValues(context);
    }
}

As you see, a converter has access to the property grid context to get the values from somewhere. This is what's displayed in this case: