How to create a private class method?

How come this approach of creating a private class method works:

class Person

  def self.get_name
    persons_name
  end

  class << self

    private

    def persons_name
      "Sam"
    end
  end
end

puts "Hey, " + Person.get_name
puts "Hey, " + Person.persons_name  #=> raises "private method `persons_name' called for Person:Class (NoMethodError)"

But this does not:

class Person

  def self.get_name
    persons_name
  end

  private

  def self.persons_name
    "Sam"
  end
end

puts "Hey, " + Person.get_name
puts "Hey, " + Person.persons_name