because you have to use a middleware for it and use $middlewarePriority to re-config cookie name before initializing cookies.
You can't change cookie's name after they are outputed to the respone headers. (Technically)
protected $middlewarePriority = [
\Illuminate\Foundation\Http\Middleware\HandlePrecognitiveRequests::class,
\Illuminate\Cookie\Middleware\EncryptCookies::class,
// Domain or SubDomain or Tenant Cookie Modifier Middleware Here
\Illuminate\Cookie\Middleware\AddQueuedCookiesToResponse::class,
\Illuminate\Session\Middleware\StartSession::class,
\Illuminate\View\Middleware\ShareErrorsFromSession::class,
\Illuminate\Contracts\Auth\Middleware\AuthenticatesRequests::class,
\Illuminate\Routing\Middleware\ThrottleRequests::class,
\Illuminate\Routing\Middleware\ThrottleRequestsWithRedis::class,
\Illuminate\Contracts\Session\Middleware\AuthenticatesSessions::class,
\Illuminate\Routing\Middleware\SubstituteBindings::class,
// Spatie Team Middleware Here
\Illuminate\Auth\Middleware\Authorize::class,
];
keep in mind that you should use that middleware somewhere to activate this priority. somewhere like routes vie $middlewareAliases or direct class names.
Good luck