Generally, best practice is to set up one vendor record per legal entity and include the DBAs in that one record. The driver is tax reporting – you must report payments to the legal entity, though you may write checks to the DBAs. If the DBAs are merely DBAs, then you are paying a single entity and must report the sum total of payments to it. You can set them up separately but connect them and ensure reporting is complete.
On the other hand, if rather than DBAs, the multiple companies are actually each legal entities that have the same parent company, each legal entity should be set up separately. It is considered best practice for a couple of reasons. Again, tax reporting is a key driver; assuming that each entity is operating as a discrete business and bill at that level, it makes sense for accounting, record-keeping/history, vendor relations, and payment reporting. But again, you want to link the entities in the vendor master file since it is important to understand the relationships each has with the parent and each other.
Leading ERPs allow links between related entities. For example, the first several digits of the vendor ID will be identical and establish the linkage between entities, for example "18045"; the remaining digits of the vendor ID will identify each particular entity, e.g., the parent entity would end in 001 (18045001 or 18045-001), and the individual entities would end in 002, 003, 004, etc., all linked to the 18045 root. If a company's ERP does not allow that, then typically the comment field should be used to identify parent & sibling relationships.