How to restrict few linq features/ lampda query for my C# collection

public class Person
{
	private string personname = string.Empty;
	private DateTime dob = new DateTime(1900,1,1);
	
	public Person(){} //default empty constructor
	
	public Person(string _name, DateTime _dob)
	{
		personname = _name;
		dob = _dob;
	}
	
	public string Name
	{
		get => personname;
		set => personname = value;
	}
	
	public DateTime DateOfBorn
	{
		get => dob;
		set => dob = value;
	}
	
	public int Age => DateTime.Today.Year - this.dob.Year;
	
}

public class RestrictedCollection
{
	private List<Person> persons = null;

	public RestrictedCollection()
	{
		persons = new List<Person>()
		{
			new Person("Adam", new DateTime(1984,1,1)), new Person("Bart", new DateTime(1972,10,11)),
			new Person("Celine", new DateTime(1983,12,13)), new Person("Dijon", new DateTime(1986,3,17)),
			new Person("Eveline", new DateTime(1979,9,1)), new Person("Elisabeth", new DateTime(1985,5,21)),
			new Person("Ferdinand", new DateTime(1978,11,1)), new Person("Friderik", new DateTime(1979,7,31))
		};
	}
	
	public void Add(Person p)
	{
		if(!persons.Contains(p))
			persons.Add(p);
		else
			throw new InvalidOperationException($"'{p.Name}' born at {p.DateOfBorn.ToString("yyyy-MM-dd")} already exists!");
	}
	
	public void Remove(Person p)
	{
		if(persons.Contains(p))
			persons.Remove(p);
		else
			throw new InvalidOperationException($"'{p.Name}' born at {p.DateOfBorn.ToString("yyyy-MM-dd")} does not exist!");
	}
	
	public List<Person> Filter(Func<Person, bool> predicate)
	{
		List<Person> filtered = persons.Where(predicate).ToList();
		return filtered;
	}

}

void Main()
{
	RestrictedCollection rc = new RestrictedCollection();
	//find persons 
	var result = rc.Filter(x=>x.Name.StartsWith("F"));

	//add new person
	Person p = new Person("Maciej", new DateTime(1969, 12, 6));
	rc.Add(p);
	result = rc.Filter(x=>x.Name==p.Name);
	
	//try to add existing person
	rc.Add(p); //throws InvalidOperation exception!
}