What a stupid question, the majority would say. When I talk to a person, I relate with a person, not a brand.
Not really. Understanding brands better brings you closer to the notion that animals relate among animals while people also relate to brands that form the space around them.
This question goes far beyond the usual marketing considerations of branding. It is a question of philosophy, a question of identity, and a question of how humans relate in the objective world. Branding has not much to do with marketing.
Let me make the answer as simple as possible. After you, as a living creature, die, your brand keeps living, at least for some time. As a physical body, you follow the laws of physics, biology, and genetics. Conversely, your brand follows laws of memetics, cultural inheritance, and other laws specific to humans as memetic creatures.
Your brand does not disappear alongside your body (tied to laws of entropy) but keeps living fuelled by energy accumulated based on laws of memetics. Some brands like God, Aristotle, or Mozart have such internal power that they live for ages after the subject that originated them died.
What is especially curious about long-lasting personal brands is that they can almost indefinitely rebrand. What other than constant rebranding occurs each time a brand is consumed by its user? That some brands die in a matter of days after their body lose their property of life means that their memetic/branding properties were unable to rebrand.
Now, we can jump to the initial question of whether we interact with our environment as subjects (me) or as brands.
You do interact with other humans physically, but you can not avoid interacting with them on memetic levels as long as you are human.
Duality of interactions
How do we explain this duality? There is a peculiar environment in which humans interact only on a memetic level, utterly detached from the physical reality of our bodies: the virtual reality of social media. There, you interact with others only on the memetic, brand level.
So the answer is that you relate with people as brands only on a memetic level, but that does not mean that you do not relate with them on a physical genetic level.
Brandlife develops this issue from various