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.

But that's on OpenAI for selecting that company name. EU trademark law hasn't changed, this was always going to be a problematic trademark if challenged

They still have the trademark on their logo

If I search for "Open AI" on google right now the first search results are openai.com, chatgpt.com and the OpenAI wikipedia page. None of which are open AI.