Here, I'll rephrase thenoblesunfish for clarity, because you seem to have misread

  > Is this why the Google product (now just called Gemini) was called [Bard]?

"That" == "Bard".

They weren't referring to Gemini, which is why there's that whole thing in parentheses stating it's *now* called Gemini

From Wiki

  | The technology was developed under the codename "Atlas", with the name "Bard" in reference to the Celtic term for a storyteller and chosen to "reflect the creative nature of the algorithm underneath".