using System;

using Newtonsoft.Json;

using System.Linq;

using System.Collections.Generic;

public class Program

{

    public static void Main()

    {

        string json = @"[{

            ""Id"": 123,

            ""Name"": ""Admin"",

            ""Group"": 1,

            ""OldValue"": 2,

            ""LastestValue"": 1

            },

            {""Id"": 123,

            ""Name"": ""Admin"",

            ""Group"": 1,

            ""OldValue"": 0,

            ""LastestValue"": 1

            },

            {""Id"": 456,

            ""Name"": ""Worker"",

            ""Group"": 2,

            ""OldValue"": 0,

            ""LastestValue"": 1

            }]";

        List<Root> roots = JsonConvert.DeserializeObject<List<Root>>(json);

        var result = roots.GroupBy(x => x.Name)

            .Select(g => new

                    {

                        Name = g.Key,

                        Data = g.First().LastestValue == g.Last().LastestValue

                            ? g.Last()

                            : null

                    })

            .Select(x => x.Data)

            .Where(x => x != null)

            .ToList();

        Console.WriteLine(JsonConvert.SerializeObject(result, Formatting.Indented));

    }

}

​

public class Root

{

    public int Id { get; set; }

    public string Name { get; set; }

    public int Group { get; set; }

    public int OldValue { get; set; }

    public int LastestValue { get; set; }

}