Not sure this is the "simplest, most readable way" but
$key = $users->search(function ($user, $key) use ($search4me) {
return $user->name === $search4me;
});
$this->id = $users->get($key)->id;
I've just made it up after a quick search at the documentation ( https://laravel.com/docs/5.3/collections#available-methods ). If you are going to use it, make sure you cover the cases where nothing will match your search/key etc. Also note that the search() will return you the first match.
And one note on your code: it assume that your items in the database will always have the correct id order but in real applications that is not the case because imagine you delete some record, or some transaction fail (it will preserve the ids before rollback), etc. What I mean by example: if your collection contains 200 items, they must be with ids of 0-199 or the $key++; part of your code will fail.