Use HashSet<T>.Add with a custom EqualityComparer<T> to efficiently find duplicates

GetDistinctDuplicates.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            var items = new List<Item>() {
                new Item() { Name = "test" },
                new Item() { Name = "test" },
                new Item() { Name = "test" },
                new Item() { Name = "test2" },
                new Item() { Name = "test2" },
                new Item() { Name = "test3" }
            };
            var duplicates = GetDistinctDuplicates(items, new ItemNameComparator());

            Console.WriteLine(String.Join(", ", duplicates.Select(i => i.Name)));
            Console.ReadLine();
        }

        public class Item
        {
            public string Name { get; set; }
        }

        public static IEnumerable<T> GetDistinctDuplicates<T>(IEnumerable<T> items, IEqualityComparer<T> comparator)
        {
            HashSet<T> doops = new HashSet<T>(comparator);
            return items.Where(p => !doops.Add(p)).Distinct(comparator);
        }

        public class ItemNameComparator : EqualityComparer<Item>
        {
            public override bool Equals(Item item1, Item item2)
            {
                return (item1 == null ? "" : item1.Name).ToUpperInvariant().Equals((item2 == null ? "" : item2.Name).ToUpperInvariant());
            }

            public override int GetHashCode(Item item)
            {
                return (item == null ? "" : item.Name).ToUpperInvariant().GetHashCode();
            }
        }
    }
}