I'm still processing Iron Lung as a whole but now that I think about it more that moment where Ava and Simon reveal their names to each other is just. So damn good and beautiful.
The movie is just so miserably (emotionally) for everyone involved. Ava is cold, she's solely focused on trying to survive, picking and choosing the calculated risks that need to be made towards that goal. Every person is a resource, one that is limited and dwindling. She doesn't, and shouldn't, in this situation, care who "the Convict" is, especially not this one, after what he did. There is no reason to know his name, no reason to see a person in what is essentially just their living camera. Simon is barely meant to be a person now, a Convict first, a "Butcher" second. He would be as abandoned in a prison cell as he is in the SM-13. Conceptually, the two are the same place. He is a living tool waiting to die, even if told otherwise.
Everybody suffers, whether they're in the blood ocean or not. In a way, all the people in the Consolidation may be no different from Simon himself, just floating around in a metal vessel waiting to die at the hands of some greater force that dwarfs them all, one that is beyond their comprehension. In the face of that, can one's own name even matter? What worth is offering humanity when everyone needs to fight tooth and nail just for the hope to live? Everyone is, I'm sure, going through the same slow descent into hopeless madness that Simon is, just at different rates, and with the way things are currently it's warranted. It may even be inevitable.
But in the midst of all that madness, there's just a moment of something slower, gentler. It's sympathy, maybe, or some form of understanding.
You hear Ava falter when Simon expresses how much of nothing he's become ("You sent me down here to die and you don't even know my name?"). In the face of the Quiet Rapture, or even the monster on AT-5, everyone's a nobody. They either become part of the void or another faceless echo in the cacophony that lives in the blood ocean. But then, out of her own volition, Ava offers her own name, a subtle invitation for Simon to offer his back. In that moment, they exist as people again. Yes, it's still under the guise of what is ultimately a bargain and an act of mutual benefit, but that specific action of offering one's name, especially from Ava specifically, is one done out of real sincerity. A brief flicker of humanity in a world where all it has left to do is die.
That entire part of their exchange is 20 seconds long in a 2 hour film. It's quiet. It's a giving of pause, a reprieve, in a scene that builds up anticipation and stress. Simon and Ava don't even see each other in that moment. For all Simon, or Ava, or, hell, even the viewer knows, the voice on the other end might not even be real. Another hallucination, a trick in the systems. In the grand scheme of things, it's a 20 seconds wasted. Time is of the absolute essence with this new objective, and just because Simon's miraculously alive now doesn't mean he couldn't run out of oxygen, or the ship couldn't suddenly crumble under pressure, or some unknown entity couldn't make the line go dead once more. But the moment is still afforded time, and therefore afforded importance. It's a moment savored (and therefore imo wonderfully paced).
It doesn't matter, ultimately, that Ava and Simon learn each others names. They really are wiped out like they are nothing, just like the stars, just like the rest of the world, specks of dirt, a blip on the radar that fades away without anyone around to hear its final sound. But for that moment, they got to be people. They got to be more than the clawing instinct for survival, the descent into madness, more than the incomprehensible rapture or whatever higher beings may or may not be up there, in their own way. They just got to be people, seeing eye to eye, with names and faces and feelings and pauses that mattered more than the constant forward momentum of trying to stay alive, just for 20 seconds.
In the end, "It's more than me. It's more than you." but, for just a moment, existing as just "me" and "you" was enough.