Gemini's inspiration was the "gopher" protocol from the early 1990s. Gopher was a text-only precursor to the web - plain text with highlighted clickable text links. If you've ever used an ancient library computer (green and black display), their UI was essentially the same as gopher.
To be fair, names based on Greek and Roman mythology were overplayed back when NASA was using them. Calling anything "Gemini" is about as uncreative as one can get.
