class Tracker
  @@names = []

  def self.names
    @@names
  end

  def initialize(name)
    @name = name
    @@names << name
  end
end

2.6.3 :013 > Tracker.new("Vasya")
 => #<Tracker:0x00007fffb9525bc8 @name="Vasya">
2.6.3 :014 > Tracker.new("Petya")
 => #<Tracker:0x00007fffb9528cb0 @name="Petya">
2.6.3 :015 > Tracker.names
 => ["Vasya", "Petya"]

require 'debug_inspector'

class User
  def self.variable_names
    RubyVM::DebugInspector.open do |inspector|
      variables = eval("local_variables", inspector.frame_binding(2))
      variables.map!(&:to_s)
      variables.select do |x|
        eval(x, inspector.frame_binding(2)).is_a?(self)
      end
    end
  end
end

user1 = User.new
user2 = User.new

pp User.variable_names