How to rename array keys in PHP?

You could use array_map() to do it.

$tags = array_map(function($tag) {
    return array(
        'name' => $tag['name'],
        'value' => $tag['url']
    );
}, $tags);

Loop through, set new key, unset old key.

foreach($tags as &$val){
    $val['value'] = $val['url'];
    unset($val['url']);
}

Talking about functional PHP, I have this more generic answer:

    array_map(function($arr){
        $ret = $arr;
        $ret['value'] = $ret['url'];
        unset($ret['url']);
        return $ret;
    }, $tag);
}