It sounds like you're thinking of the adjective form of the word, which is why you are thinking of a much broader definition. I was using the noun form, since Gemini are noun twins.
If we were talking about the word "twins" in the abstract, the broader definition might make sense. But we aren't — we're talking about Gemini. If that conjures up general notions of "matched-ness" for you, that's great. When I think about Gemini, I think about mythological twins. I don't think about corresponding parts that complement each other.
For a product name to be successful, it should appeal to a wide range of people. If I'm way out in left field on this one, perhaps they've found a great name. But I would point out that my comment, which is critical of the name change, is the very first comment in the entire thread. I would take that as evidence that most people don't see the name and think "oh, it's like complementary items, like my brain and the AI".
To be clear, I was shocked to see this comment above all substantive discussion of the new release. I would have thought it would have been buried under examples of ways in which Ultra is better/worse than some other LLM.