Do the companies share the same data (a) just for read access (b) for read/write? Should each be able to see the other's data?

One solution if they don't need to share data at all is just to give them different schemas to connect to and to duplicate the table structures (but not the data) in each schema.

If they need to share data then the shared data can go into a schema accessible by both. but they should still both have their own schema for security/tracking purposes.

Or they could both connect to the same schema, but if they do that then each company will have full control over the other company's data, which may not be desirable.