There used to be Bard but no one remembers it anymore (although this is a bit different, because Bard wasn't nearly as well known as Gemini).

I'm really curious if OpenAI wanted to adopt a different name at some point. Or maybe they hope that sometime in the future one of their products will supersede ChatGPT and everyday people will start using that new name for everything AI so maybe they aren't in a rush to rename ChatGPT itself to anything else.

It seems like they have dropped ChatGPT in favour of just GPT... And they are going pretty hard with Astra/Sol/Luna too. So I guess they'll go with those if they're successful.

They're definitely missing a good unifying name like Claude though. (RIP anyone called Claude - when are companies going to stop fucking people over by giving popular products existing human names?)