Please Review this Code

The name and the age of a person should be read-only. Name changes should be covered by methods like ChangeName(). The age is a calculated value depending on the birthdate.

Also make the GetOldest() method a little bit more robust:

namespace CsharpExamples
{
    using System;
    using System.Collections.Generic;
    using System.Linq;

    class Person
    {
        public int Age
        {
            get
            {
                return DateTime.Now.Subtract(this.Birthdate).Days / 365;
            }
        }

        public DateTime Birthdate { get; private set; }
        public string Name { get; private set; }

        public Person(string name, DateTime birthdate)
        {
            this.Birthdate = birthdate;
            this.Name = name;
        }

        public override string ToString()
        {
            return string.Format("{0}:{1}", this.Name, this.Age);
        }
    }

    class PersonPopulation
    {
        private readonly List<Person> persons = new List<Person>();

        public int Count
        {
            get
            {
                return this.persons.Count;
            }
        }

        public Person GetOldest()
        {
            return this.persons.OrderByDescending(x => x.Age).FirstOrDefault();
        }

        public void Add(params Person[] persons)
        {
            this.persons.AddRange(persons);
        }
    }

    class Test
    {
        public static void Main()
        {
            var population = new PersonPopulation();
            var person1 = new Person("Ayoub", new DateTime(1990, 1, 1));
            var person2 = new Person("Saeed", new DateTime(1995, 1, 1));
            var person3 = new Person("Mahdi", new DateTime(2000, 1, 1));

            Console.WriteLine("Oldest Person is --> " + population.GetOldest());

            population.Add(person1, person2, person3);

            Console.WriteLine("Oldest Person is --> " + population.GetOldest());
            Console.WriteLine("population: " + population.Count);
            Console.ReadLine();
        }

    }
}

You can implement the GetOldest() method either as method as you did or as property. I don't favorite any. But when you name methods: Get and Set are reserved verbs for explicit getter and setter methods. So FindOldestPerson() is a slightly better name.