I agree with your friend.

Unless they are non-organic because they were deliberately built that way, mechanoid doesn't make much sense. Where would mecha- as a prefix come from to them?

They'd be mystified by 'the flesh' and wonder how it manages to operate. (see the story They're Made of Meat.)

I have no good insight at the moment how they might refer to themselves except maybe by chemical composition.

I l've always imagined that a silicon based life-form (one of the few realistically proposed possibilities of inorganic life I know of) just sounds like a crystal chandelier during an earthquake.

Linguistically, whatever they name themselves in their own language would just translate to whatever we call them in our languages because that's usually what we do. I think this would be especially true if the alien language is physically impossible to vocalize as a human.

Yeah, I'm going to be in agreement with your friend.

It's also worth noting that even within "inorganic" species, there might be stark differences in their internal composition (and thus view of themselves). Are these an animate silicon crystal, or a "robot person"? The former might think of themselves as "the solid", in contrast to liquid-containing non-silicon life.

They might also (in either case) use a name which reflects their local name for whatever the dominant element or feature is their makeup, similar to how we refer to Earthly life as "cellular" life because it's made of cells. That said, "Mechanoids" as a foreign nickname or slur might be a fun thing.

Kind of depends on the history and culture and how they are programed to interact with each other. They might not even name themselves with a physical description. "The Created" could be accurate too.

I put your question into ChatGPT to see what it would come up with, I think there are some good potentials in here:

The concept of inorganic species naming themselves involves a blend of creative linguistics and speculative fiction. The term "mechanoid" is indeed a common and somewhat generic term in science fiction to refer to robotic or mechanical beings. If we consider that an inorganic species might develop its own sense of identity and culture, they could potentially adopt a name that reflects their unique characteristics and philosophical perceptions. Here are some inventive alternatives to "mechanoid" and the thought processes that might lead an inorganic species to choose them:

1. Synthetix

Derived from "synthetic," indicating their man-made origins, combined with a twist that makes it unique and culturally specific to them. It emphasizes their artificial nature but also sounds like a name they might proudly identify with, suggesting sophistication and complexity.

2. Auracite

Combining "aura" (a term sometimes used to describe a manifest energy or presence) with "cite" (from citadel, suggesting structure), this term could denote inorganic beings who perceive themselves as both energetic and structured, emphasizing a complex framework that supports what might metaphorically be described as their soul or spirit.

3. Ferrumin

Rooted in "ferrum," the Latin word for iron, a common metal. This name could be embraced by metallic beings, emphasizing their strong, enduring nature. It connotes a sense of agelessness and durability, key traits for inorganic forms.

4. Electon

Derived from "electron," highlighting their reliance on electrical energy, this name would fit a species that views itself as inherently tied to electric or energetic phenomena. It emphasizes their dynamic and energetic essence.

5. Crystalline

For a species with a crystal-like structure, emphasizing transparency, precision, and symmetry. This name reflects physical beauty and an orderly, geometric nature, which could be central to their identity.

6. Golemics

Inspired by "golem," a mythical being animated from inanimate matter, combined with a suffix that suggests a scientific or systematic study, like "physics." This could be suitable for a species that sees itself as crafted with purpose and potential beyond mere machinery.

7. Quantix

Influenced by "quantum," reflecting a fundamental connection to physics at a microscopic scale. This could be particularly apt for a species that perceives themselves as operating on or exploiting quantum mechanical principles.

8. Silicoid

Rooted in "silicon," which is often used in electronic components and could be a base element for these beings. It emphasizes their elemental nature and could be seen as defining their "species" from a chemical standpoint.

9. Kinetix

From "kinetic," emphasizing motion and energy, this name would suit an inorganic species that values mobility and the flow of energy through their systems as central aspects of their being.

10. Neuracite

Combining "neural" (nerve, relating to the nervous system) with "cite" (implying a place or community). This could be used for a species that has developed a form of artificial intelligence or neural networks akin to a brain, emphasizing their intellectual and cognitive capacities.

Each of these names carries connotations that reflect how the species might view themselves in terms of composition, capabilities, and philosophies. In your writing, picking a name that aligns well with the species’ characteristics and the themes of your narrative can enrich world-building and add depth to the portrayal of these beings.