According to Persona's damage control article[0], the subdomain had "onyx" in its name because that's the internal code name for the project, and it's named after the pokémon Onyx. No connection to Fivecast ONYX.
Naming a fantasy creature after a common gemstone should make it non-trademarkable anyway, but I'd love to see Nintendo tie up the US government in court for years.
[0] https://withpersona.com/blog/post-incident-review-source-map...