You can also refresh the configuration in it's entirety:
ConnectionStringSettings importToConnectionString = currentConfiguration.ConnectionStrings.ConnectionStrings[newName];
if (importToConnectionString == null)
{
importToConnectionString = new ConnectionStringSettings();
importToConnectionString.ConnectionString = importFromConnectionString.ConnectionString;
importToConnectionString.ProviderName = importFromConnectionString.ProviderName;
importToConnectionString.Name = newName;
currentConfiguration.ConnectionStrings.ConnectionStrings.Add(importToConnectionString);
}
else
{
importToConnectionString.ConnectionString = importFromConnectionString.ConnectionString;
importToConnectionString.ProviderName = importFromConnectionString.ProviderName;
}
Properties.Settings.Default.Reload();