Magento – Get current store name in observer method

Finally got it.

The observer function:

public function before_product_save($observer)
{
    $product = $observer->getProduct();
    $product->setStoreId(1)->setData('visibility', 4);
}

where, the store id is 1 and the visibility attribute value 4 refers to Catalog, Search.

Take a look at Magento change product name adding to cart

Use event sales_quote_item_set_product

class Mynamespace_Samples_Model_Observer
{
    public function salesQuoteItemSetProduct(Varien_Event_Observer $observer)
    {
        /* @var $item Mage_Sales_Model_Quote_Item */
        $item = $observer->getQuoteItem();

        //only change the item you want by product id
        if($item->getProductId() == xyz){
            $item->setName('Ians custom product name');
        }

        return $this;
    }
}