Parse error: syntax error, unexpected ‘(‘, expecting ‘,’ or ‘;’ in

You can’t initialize member variables to anything that is not static, and you’re trying to call a function.

From the manual:

This declaration may include an initialization, but this
initialization must be a constant value–that is, it must be able to
be evaluated at compile time and must not depend on run-time
information in order to be evaluated.

The workaround is to set your variable in the constructor:

private $random_name;
public function __construct() { 
    $this->random_name = rand(1000,9999).rand(1000,9999).rand(1000,9999).rand(1000,9999);
}