Adding restaurants in database
As you cannot use the vendor name as identifier, since it may be duplicated (as it happens with the name of a person), you need a true identifier to be set upon creation. When someone identifies themselves in your system, they cannot identify by their name, since it is not enough to uniquely identify them. Thus you don't have any other option than assigning them any proper id when you create the record on your vendors table and identify them by that id. 

For this purpose you can create an ad-hoc column (filled in its most simple approach with an auto incremental series), or use a contact email, Tax identifier or any other key that you know is unique, instead of the name.