$array = array("Kyle","Ben","Sue","Phil","Ben","Mary","Sue","Ben");
$counts = array_count_values($array);
echo $counts['Ben'];

function array_count_values_of($value, $array) {
    $counts = array_count_values($array);
    return $counts[$value];
}

Not native, but come on, it's simple enough. ;-)

Alternatively:

echo count(array_filter($array, function ($n) { return $n == 6; }));

Or:

echo array_reduce($array, function (n) { return n == 6); }, 0);

Or:

echo count(array_keys($array, 6));

No such function exists. You always need to first map the values you would like to count (and those values must be string or integer):

$map = function($v) {return $v->name;};

$count = array_count_values(array_map($map, $data));