How to get information of a field from a magento module?

I am developing a shipping restriction plugin for magento 2, looking at the documentation I found the detailed information of the initial creation process. One of the validations I need is:

Depending on the name of the store, enable or disable a type of delivery, in the red box I show the select that allows choosing the name of the store.

From my php code I want to be able to obtain that value to activate or deactivate the send method. The following is the base code of the module that I am developing, I would like to obtain the name of the store chosen in this field to activate or deactivate a shipping type.

 public function collectRates(RateRequest $request) {
         if (!$this->isActive())
         {
             return false;
         }
         $result = $this->_rateResultFactory->create();
         $shippingPrice = $this->getConfigData('price');
         $method = $this->_rateMethodFactory->create();
         $method->setCarrier($this->getCarrierCode());
         $method->setCarrierTitle($this->getConfigData('title'));
         $method->setMethod($this->getCarrierCode());
         $method->setMethodTitle($this->getConfigData('name'));
         $method->setPrice($shippingPrice);
         $method->setCost($shippingPrice);
         $result->append($method);
            return $result;
      }

I am currently using this code to get the address, but I am not very clear how to use it to obtain the value of the select that loads the stores

 $object_manager = MagentoFrameworkAppObjectManager::getInstance();

        $get_cart = $object_manager->get('MagentoCheckoutModelCart');

        $getAdress = $get_cart->getQuote()->getShippingAddress();

        $distance = $getAdress->getData('street');