How to list the SQL Server Instances installed on a local machine? ( Only local )

Direct access to Windows Registry isn't the recommended solution by MS, because they can change keys/paths. But I agree that SmoApplication.EnumAvailableSqlServers() and SqlDataSourceEnumerator.Instance fails providing instances on 64-bit platforms.

Getting data from Windows Registry, keep in mind the difference in Registry access between x86 and x64 platforms. 64-bit edition of Windows stores data in different parts of system registry and combines them into views. So using RegistryView is essential.

using Microsoft.Win32;

RegistryView registryView = Environment.Is64BitOperatingSystem ? RegistryView.Registry64 : RegistryView.Registry32;
using (RegistryKey hklm = RegistryKey.OpenBaseKey(RegistryHive.LocalMachine, registryView))
{
    RegistryKey instanceKey = hklm.OpenSubKey(@"SOFTWARE\Microsoft\Microsoft SQL Server\Instance Names\SQL", false);
    if (instanceKey != null)
    {
        foreach (var instanceName in instanceKey.GetValueNames())
        {
            Console.WriteLine(Environment.MachineName + @"\" + instanceName);
        }
    }
}

If you are looking for 32-bit instances on a 64-bit OS (pretty weird, but possible), you will need to look:

HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\Microsoft\Microsoft SQL Server

You could call EnumAvailableSQlServers with a localOnly = True

public static DataTable EnumAvailableSqlServers(bool localOnly)

See MSDN docs for EnumAvailableSqlServers

you can use registry to get sql server instance name in local system

private void LoadRegKey()        
{            
    RegistryKey key = Registry.LocalMachine.OpenSubKey(@"SOFTWARE\Microsoft\Microsoft SQL Server\Instance Names");            
    foreach (string sk in key.GetSubKeyNames())            
    {                
      RegistryKey rkey = key.OpenSubKey(sk);                
      foreach (string s in rkey.GetValueNames())                
      {                    
         MessageBox.Show("Sql instance name:"+s);                
      }            
    }        
}

SqlDataSourceEnumerator instance = SqlDataSourceEnumerator.Instance;
System.Data.DataTable table = instance.GetDataSources();
foreach (System.Data.DataRow row in table.Rows)
        {
            if (row["ServerName"] != DBNull.Value && Environment.MachineName.Equals(row["ServerName"].ToString()))
            {
                string item = string.Empty;
                item = row["ServerName"].ToString();
                if(row["InstanceName"] != DBNull.Value ||  !string.IsNullOrEmpty(Convert.ToString(row["InstanceName"]).Trim()))
                {
                    item += @"\" + Convert.ToString(row["InstanceName"]).Trim();
                }
                listview1.Items.Add(item);
            }
        }