コード

<?php
$array = [
    ['staff' => 'name1,name2,name3,name5'],
    ['staff' => 'name4,name5,name6,name1'],
];
$result = [];
foreach ($array as $value){
    $result = array_merge($result,explode(',',$value['staff']));
}

$mergedArray = array_merge(...array_map(function($item) {
    return explode(',', $item['staff']);
}, $array));

または

$res = array_merge(...array_map(function($v){return explode(',',$v['staff']);},$array));

$res = array_merge(...array_map(fn($v) => explode(',',$v['staff']),$array));

var_dump($res);

結果2

array(8) {
  [0]=>
  string(5) "name1"
  [1]=>
  string(5) "name2"
  [2]=>
  string(5) "name3"
  [3]=>
  string(5) "name5"
  [4]=>
  string(5) "name4"
  [5]=>
  string(5) "name5"
  [6]=>
  string(5) "name6"
  [7]=>
  string(5) "name1"
}