In your Google Shopping ads, you can see the image, price, title, description, reviews and also the business name.
To change the store name, login to Google Merchant Center and go to Business information > About display name > Business display name and simply add a new name and click on save.
Before you add a new name, make sure to follow the policies to avoid any down time and disapproval’s.
If you have changed your business name and Google Shopping still has the old name, than make sure you have waited a week for the system to update. Changing the business name will not change Google Shopping instantly.
If after a week nothing has changed, get in touch with Google Adwords team.