Domain Driven Design : Can aggregate root have public setter?

If I have a aggregate root says User It have property like

public class User:BaseEntity
{


    public User()
    {
        //Ef Use
    }

    public User(string firstName, string secondName,
        string userName,Password password )
    {
        this.UserName = userName;
        this.Password = password;
        this.FirstName = firstName;
        this.SecondName = secondName;
    }

    public string UserName { get; private set;}
    public Password Password { get; private set;}
    public string FirstName { get; private set;}
    public string SecondName { get; private set;}
}

I can create new user like var naz=new User ("naz","password","firstName","secondname") and save using UserRepository . How should I edit User fistname property ?

Should I need to make public setter and Save using repository ? .

I am confused ,new to DDD .How Should I implement this .