Unable to change the default s3 driver bucket name with a new bucket in laravel

I am trying to update a profile and also trying to upload the image to a specific aws bucket. In my function, the s3 is considering the default bucket, I want to store it into a different bucket which I have created.

public function updateCustomerProfileDetails(Request $request)
    {
        $returnArray = array();

        // Validate the request data
        $request->validate([
            'first_name'                    => 'alpha:ascii',
            'last_name'                     => 'alpha:ascii',
            'profile_image'                 => 'file|image|mimes:jpeg,png,jpg,gif',
            'contact_number'                => ['regex:/^(\+\d{1,2}\s?)?\(?\d{3}\)?[\s.-]?\d{3}[\s.-]?\d{4}$/']
        ]);
        try {
            $logedUser = auth()->user();
            $user = self::loadParticuler('id', $logedUser->id);

            if ($user == null) {
                return $this->returnErrorResponse(self::COMPONENT_CODE, 114, 'User does not exist', 422);
            }

            $userDetails = $user->details;

            if ($userDetails == null) {
                $userDetails = new UserDetails();
                $userDetails->user_id = $user->id;
            }

            $root_user = RootUser::where('email', auth()->user()->email)->with('details')->first();

            $isUpdated = false;

            if (!empty($request->first_name)) {
                $userDetails->first_name = $request->first_name;
                $root_user->details->first_name = $request->first_name;
                $isUpdated = true;
            }

            if (!empty($request->last_name)) {
                $userDetails->last_name = $request->last_name;
                $root_user->details->last_name = $request->last_name;
                $isUpdated = true;
            }

            if (!empty($request->contact_number)) {
                $userDetails->mobile = $request->contact_number;
                $root_user->details->contact_number = $request->contact_number;
                $isUpdated = true;
            }

            if (!empty($request->profile_image)) {
                $env = config('app.env');
                $disk = ($env == 'production') ? 's3' : 'local';
                $url = Storage::disk($disk)->put('/'.auth()->user()->email.'/', $request->profile_image);

                $userDetails->profile_image = $url;
                $root_user->details->profile_image  = $url;
                $isUpdated = true;
            }

            if ($isUpdated) {
                $userDetails->save();
                $root_user->details->save();
            }

            $msg = $isUpdated ? "Data Updated Successfully" : "There are no changes to update";
            $returnArray['status'] = "Success";
            $returnArray['message'] = $msg;
            return response()->json($returnArray, 200);

        } catch (\Illuminate\Validation\ValidationException $e) {
            return $this->returnErrorResponse(self::COMPONENT_CODE, 115, array_column($e->errors(), 0), 422);
        } catch (\Exception $e) {
            return $this->returnErrorResponse(self::COMPONENT_CODE, 116, $e->getMessage(), 422);
        }
    }

KIndly suggest how can I change the default bucket to my specified bucket and within t a folder will be created with the email id of the user logged in in which the profile image will be saved.