Hmm, two things:
shuffling that array and accessing it from the outside, and having the outside call rely on the array being shuffled, doesn't feel right. It would be nicer to have a method that returns the result of an array shuffling, and maybe also the name straight away.
It would be good style to declare all object properties beforehand so it can be documented later. So if you use $this->name, you should declare it.
Both points implemented could look like this:
class greeting
{
protected $greet = array('Hi','Hello', 'Howzit', 'Ola', 'Whats up');
protected $name = null;
public function __construct($name)
{
$this->name = $name;
}
public function greet()
{
shuffle($this->greet);
return $this->greet[1]." ".$this->name;
}
}