ChatGPT is a household name. And OpenAi is actually not, people outside tech don't necessarily know it.
But people actively searching for AI products who are perhaps a little less technically inclined might. And if they stumble upon a platform that by all accounts seems to be affiliated with OpenAI, that could be problematic, especially with the level of trust people seem to be comfortable handing to LLMs.
Being well known is not part of determining if a trademark is valid