The following code will list all the SQL Server instances on the local machine.

            RegistryView rv = Environment.Is64BitOperatingSystem ? RegistryView.Registry64 : RegistryView.Registry32;

            using (RegistryKey hklm = RegistryKey.OpenBaseKey(RegistryHive.LocalMachine, rv))
            {
                RegistryKey rk = hklm.OpenSubKey(@"SOFTWARE\Microsoft\Microsoft SQL Server\Instance Names\SQL", false);
                if (rk == null) return;

                foreach(var v in rk.GetValueNames())
                {
                    Console.WriteLine($"{v} : {rk.GetValue(v)}");
                }
            }

            Console.ReadLine();

… assuming the registry is correct