Is it true that Vishnu, Siva and Durga are proper names, whereas "Brahma" is a title?
You are correct that Vishnu, Siva and Durga are divine persons. They are energies of the Lord and eternally manifest. Siva is his own tattva, or category of existence. He exists eternally and is not of the material energy. When the material world is annihilated, Siva and Vishnu remain. Durga Devi is an expansion of Krishna's internal energy. In order to manage the material energy, she is manifest as Durga Devi. She is the eternal consort of Lord Siva.
Brahma, on the other hand, is a position occupied by a jiva soul, in other words, a soul like you or me. We're also spiritual energy, but very small. We can become covered by the material energy. When the material energy is unmanifest, Brahma is also unmanifest. Also, there are many Brahmas who manage the various universes within the material world. So there are many positions available. Very advanced devotees who earn that post take up those positions.
I hope this is helpful.