display list of custom objects as a drop-down in the PropertiesGrid

In general, a drop down list in a property grid is used for setting the value of a property, from a given list. Here that means you should better have a property like “Benchmark” of type IBenchmark and a possible list of IBenchmark somewhere else. I have taken the liberty of changing your Analytic class like this:

public class Analytic
{
    public enum Period { Daily, Monthly, Quarterly, Yearly };
    public Analytic()
    {
        this.Benchmarks = new List<IBenchmark>();
    }

    // define a custom UI type editor so we can display our list of benchmark
    [Editor(typeof(BenchmarkTypeEditor), typeof(UITypeEditor))]
    public IBenchmark Benchmark { get; set; }

    [Browsable(false)] // don't show in the property grid        
    public List<IBenchmark> Benchmarks { get; private set; }

    public Period Periods { get; set; }
    public void AddBenchmark(IBenchmark benchmark)
    {
        if (!this.Benchmarks.Contains(benchmark))
        {
            this.Benchmarks.Add(benchmark);
        }
    }
}

What you need now is not an ICustomTypeDescriptor, but instead a TypeConverter an an UITypeEditor. You need to decorate the Benchmark property with the UITypeEditor (as above) and the IBenchmark interface with the TypeConverter like this:

// use a custom type converter.
// it can be set on an interface so we don't have to redefine it for all deriving classes
[TypeConverter(typeof(BenchmarkTypeConverter))]
public interface IBenchmark
{
    string ID { get; set; }
    Type Type { get; set; }
    string Name { get; set; }
}

Here is a sample TypeConverter implementation:

// this defines a custom type converter to convert from an IBenchmark to a string
// used by the property grid to display item when non edited
public class BenchmarkTypeConverter : TypeConverter
{
    public override bool CanConvertTo(ITypeDescriptorContext context, Type destinationType)
    {
        // we only know how to convert from to a string
        return typeof(string) == destinationType;
    }

    public override object ConvertTo(ITypeDescriptorContext context, CultureInfo culture, object value, Type destinationType)
    {
        if (typeof(string) == destinationType)
        {
            // just use the benchmark name
            IBenchmark benchmark = value as IBenchmark;
            if (benchmark != null)
                return benchmark.Name;
        }
        return "(none)";
    }
}

And here is a sample UITypeEditor implementation:

// this defines a custom UI type editor to display a list of possible benchmarks
// used by the property grid to display item in edit mode
public class BenchmarkTypeEditor : UITypeEditor
{
    private IWindowsFormsEditorService _editorService;

    public override UITypeEditorEditStyle GetEditStyle(ITypeDescriptorContext context)
    {
        // drop down mode (we'll host a listbox in the drop down)
        return UITypeEditorEditStyle.DropDown;
    }

    public override object EditValue(ITypeDescriptorContext context, IServiceProvider provider, object value)
    {
        _editorService = (IWindowsFormsEditorService)provider.GetService(typeof(IWindowsFormsEditorService));

        // use a list box
        ListBox lb = new ListBox();
        lb.SelectionMode = SelectionMode.One;
        lb.SelectedValueChanged += OnListBoxSelectedValueChanged;

        // use the IBenchmark.Name property for list box display
        lb.DisplayMember = "Name";

        // get the analytic object from context
        // this is how we get the list of possible benchmarks
        Analytic analytic = (Analytic)context.Instance;
        foreach (IBenchmark benchmark in analytic.Benchmarks)
        {
            // we store benchmarks objects directly in the listbox
            int index = lb.Items.Add(benchmark);
            if (benchmark.Equals(value))
            {
                lb.SelectedIndex = index;
            }
        }

        // show this model stuff
        _editorService.DropDownControl(lb);
        if (lb.SelectedItem == null) // no selection, return the passed-in value as is
            return value;

        return lb.SelectedItem;
    }

    private void OnListBoxSelectedValueChanged(object sender, EventArgs e)
    {
        // close the drop down as soon as something is clicked
        _editorService.CloseDropDown();
    }
}