class SQL
{
    private $_connection;

    public function __construct( $database = 'default-database', $hostname = 'default-hostname' )
    {
        $this->hostname = $hostname;
        $this->username = 'default-user';
        $this->password = 'default-password';
        $this->database = $database;

        $this->_connection = new \mysqli
        (
            $this->hostname,
            $this->username,
            $this->password,
            $this->database
        );
    }

    public function __destruct()
    {
        mysqli_close( $this->_connection );
    }

    public function execute( $query )
    {
        return $this->getConnection()->query( $query );
    }

    private function getConnection()
    {
        if ( !$this->_connection )
            die( 'Connection not initialized, aborting..' );

        return $this->_connection;
    }
}

// -----------

$sql = new SQL( 'different-database' );

OR

$sql = new SQL( 'different-database', 'different-hostname' );

but downside is that you can't only change hostname without providing database, or you have to write this in constructor:

    public function __construct( $database = null, $hostname = null )
    {
        $this->hostname = 'default-hostname';
        $this->username = 'default-user';
        $this->password = 'default-password';
        $this->database = 'default-database';

        if( $database !== null )
             $this->password = $database;

        if( $hostname !== null )
             $this->hostname = $hostname;

        $this->_connection = new \mysqli
        (
            $this->hostname,
            $this->username,
            $this->password,
            $this->database
        );
    }

but then you still have to write:

$sql = new SQL( null, 'hostname' );

which is bad