How to account for single name in C#?

var entityFirst = myUniqueInstance.SingleOrDefault(p => p.FirstName == newPersonFirst.FirstName && p.FamilyName == newPersonFirst.FamilyName);
if (entityFirst != null)
{
    // We found an existing person in the List of objects that matches our condition
    Console.WriteLine($"Rejected First: {newPersonFirst}");
    throw new Exception($"Person {newPersonFirst} already exists in our List!");
}
else
{
    // We did NOT find an existing person that matches out conditions
    // Now it is "pretty" save to add this person
    myUniqueInstance.Add(newPersonFirst);
    Console.WriteLine($"Added First: {newPersonFirst}");
}

using System;
using System.Collections.Generic;
using System.Linq;

namespace FindIfRecordExist
{
    public class MyUniqueClass
    {
        public int MyUniqueClassID { get; set; }
        public string FirstName { get; set; }
        public string FamilyName { get; set; }

        public MyUniqueClass()
        {
        }

        public MyUniqueClass(string FirstName, string FamilyName)
        {
            this.FirstName = FirstName;
            this.FamilyName = FamilyName;
        }

        public override string ToString()
        {
            //return $"{MyUniqueClassID} {FirstName} {FamilyName}";
            return $"{FirstName} {FamilyName}";
        }
    }


    class Program
    {
        static void Main(string[] args)
        {
            try
            {
                // This example is made with a list but this works in Entity Framework
                // And many other solution when LINQ is involved, check You 
                // include "using System.Linq;" 
                List<MyUniqueClass> myUniqueInstance = new List<MyUniqueClass>();

                myUniqueInstance.Add(new MyUniqueClass("Donald", "Truman"));
                myUniqueInstance.Add(new MyUniqueClass("Ronald", "Clinton"));
                myUniqueInstance.Add(new MyUniqueClass("Bill", "Reagan"));
                myUniqueInstance.Add(new MyUniqueClass("Hillary", "Bold"));

                foreach(var p in myUniqueInstance)
                {
                    Console.WriteLine($"Added: {p}");
                }

                try
                {
                    MyUniqueClass newPersonFirst = new MyUniqueClass("Raymond", "Kennedy");

                    // Check if there is already anyone with the same name as our new person
                    var entityFirst = myUniqueInstance.SingleOrDefault(p => p.FirstName == newPersonFirst.FirstName && p.FamilyName == newPersonFirst.FamilyName);
                    if (entityFirst != null)
                    {
                        // We found an existing person in the List of objects that matches our condition
                        Console.WriteLine($"Rejected First: {newPersonFirst}");
                        throw new Exception($"Person {newPersonFirst} already exists in our List!");
                    }
                    else
                    {
                        // We did NOT find an existing person that matches out conditions
                        // Now it is "pretty" save to add this person
                        myUniqueInstance.Add(newPersonFirst);
                        Console.WriteLine($"Added First: {newPersonFirst}");
                    }

                }
                catch (Exception ex)
                {
                    Console.WriteLine(ex.Message);
                }



                // ------------------------------------------------------------
                // Now lets run this again and se if our new person exists....
                // ------------------------------------------------------------

                try
                {
                    MyUniqueClass newPersonSecond = new MyUniqueClass("Raymond", "Kennedy");

                    // Check if there is already anyone with the same name as our new person
                    var entitySecond = myUniqueInstance.SingleOrDefault(p => p.FirstName == newPersonSecond.FirstName && p.FamilyName == newPersonSecond.FamilyName);
                    if (entitySecond != null)
                    {
                        // We found an existing person in the List of objects that matches our condition
                        Console.WriteLine($"Rejected Second: {newPersonSecond}");
                        throw new Exception($"Person {newPersonSecond} already exists in our List!");
                    }
                    else
                    {
                        // We did NOT find an existing person that matches out conditions
                        // Now it is "pretty" save to add this person
                        myUniqueInstance.Add(newPersonSecond);
                        Console.WriteLine($"Added Second: {newPersonSecond}");
                    }


                }
                catch (Exception ex)
                {
                    Console.WriteLine(ex.Message);
                }




        }
            catch(Exception ex)
            {
                Console.WriteLine(ex.Message);
            }

        }
    }
}