Laravel paginate, changing the query string to search

Currently trying to paginate some results on a product object.

The paginate object that I am receiving in my view {{ $products->links() }} is returning correctly however instead of the query being "test.com/search?search=test&page2" it is returning "test.com/search?query=test&page2" how can i change it so it returns search instead of query?

The html output is:

<a href="http://test.dev/search?query=test&amp;page=2">2</a>

but what i need is:

<a href="http://test.dev/search?search=test&amp;page=2">2</a>

EDIT: Controller:

public function searchable(Request $request)
{

    // search database, with result, list on page, with links to products,
    $products = Product::search($request->search)->paginate(3);

    return view('search.index', compact('products', 'request'));
}


use Laravel\Scout\Searchable;
use Illuminate\Database\Eloquent\Model;
use Carbon\Carbon;

class Product extends Model
{
use Searchable;

/**
 * Creates searchable index for product model
 * @return [type] [description]
 */
public function searchableAs()
{
    return 'products_index';
}
}

form:

{{ Form::open(array('url' => '/search', 'method' => 'GET', 'files' => 'false')) }}
    <div class="row">
        <div class="col-md-2">
            <button type="submit" class="custom-search-button btn btn-lrg btn-primary">Search</button>
        </div>
        <div class="col-md-10">
            <input class="search-bar" type="search" name="search" placeholder="type keyword(s) here" />
        </div>
    </div>
    {{-- <input type="hidden" name="${_csrf.parameterName}" value="${_csrf.token}"/> --}}
{{ Form::close() }}