Do I implement multiple databases for a multi-company site?

So, I have this project that will be serving several independent businesses , it is web based and its intended to serve small businesses in accounting. in my opinion maintaining a single database and attaching a unique identifier for each business might be an overkill to the database while searching for records, am thinking of implementing a single database that will track users and their linked database info, so that each user will be mapped to their owns' database.

So, if the system will end up having 'n' users, it will have 'n+1' databases__\_ where the '+1' is the main database instead of having one database for all the businesses('x1n__b_\' where 'x\_' is the unique identifier for each business, '1n' is the tracking registration number and b is the business name that will be embedded on each record for query purposes__). What is the best way to implement such? Is the 'n+1' or the 'x1n__b_'