Entity Framework 6: Clone object except ID

MyDbContext.cs

using System.ComponentModel.DataAnnotations.Schema;
using System.Data.Entity;

namespace ConsoleApplication1
{
    public class MyDbContext : DbContext
    {
        public MyDbContext()
            : base("name=MyDbContext")
        {
            Database.SetInitializer(new DropCreateDatabaseAlways<MyDbContext>());
        }

        protected override void OnModelCreating(DbModelBuilder modelBuilder)
        {
            base.OnModelCreating(modelBuilder);

            modelBuilder.Entity<MyEntity>()
                .HasKey(m => m.Id)
                .Property(m => m.Id)
                .HasDatabaseGeneratedOption(DatabaseGeneratedOption.Identity);
        }

        public virtual DbSet<MyEntity> MyEntities { get; set; }
    }

    public class MyEntity
    {
        public int Id { get; set; }
        public string Name { get; set; }
        public string CopyField { get; set; }
    }
}

Program.cs

namespace ConsoleApplication1
{
    internal class Program
    {
        private static void Main()
        {
            using (var db = new MyDbContext())
            {
                db.MyEntities.Add(new MyEntity
                {
                    Name = "Hello",
                    CopyField = "CopyMe"
                });

                db.SaveChanges();
            }

            using (var db = new MyDbContext())
            {
                var model = db.MyEntities.Find(1);
                model.Name = "Hello World";
                db.MyEntities.Add(model);
                db.SaveChanges();
            }
        }
    }
}