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Being well known is not part of determining if a trademark is valid
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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.
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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

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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.
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