how to ask user to enter alphabetic characters in c#

I'm trying to create a program that asking users to enter their name which it has to be < 30 characters and can not to be empty or numeric value .The problem is when I'm running it even if i enter a numeric value it says "name successfully accepted".I really do not know where i'm doing wrong .if You could help i really appreciate it.

 String name ;

        bool testname = true;


        while (testname)
        {
            Console.WriteLine("plz enter a name");
            name = Console.ReadLine();

            if (name.Length < 30 && name.Length == 0)
            {
                Console.WriteLine("the input can not be more  30 character or empty  ");

            }
            else
            {
                bool numeric = true;
                int checkname;
                numeric = Int32.TryParse(name, out checkname);
                if (numeric == false)
                {
                     Console.WriteLine(" name  successfully accepted");
                    testname= false;

                }
                else
                {
                    Console.WriteLine("Please enter alphabetic characters only");
                }

                Console.ReadKey();
            }



        }