As i see only 'fixed' place with First Name-Last Name is the Contact Seller box on listing details page and also some emails.

The rest of the places can be regulated with Account Form Builders (Browse form and 'Alphabetic search priority field')

Yes, we of course interested to make the software perfect powerful and flexible, but as for me issue is not so important to create a separate manager or function.

My proposed solution is to use Alphabetic search priority field as priority field also for "Dealer name" (let's call it so).

Rename it appropriately - "Dealer name and alphabetic search field" and use as first choice for Dealer name building, if not available then use current logic - First name + Last name > Username