Strange that you don't think his twitter account helped him get all that media attention along the way.
There was a legal agreement that allows him to call himself that:
> The company was incorporated as Tesla Motors, Inc. on July 1, 2003, by Martin Eberhard and Marc Tarpenning.[12][13] Eberhard and Tarpenning served as CEO and CFO, respectively.[14] Eberhard said that he wanted to build "a car manufacturer that is also a technology company", with its core technologies as "the battery, the computer software, and the proprietary motor".[15]
> Ian Wright was Tesla's third employee, joining a few months later.[12] In February 2004, the company raised US$7.5 million (equivalent to $12 million in 2022) in series A funding, including $6.5 million (equivalent to $10 million in 2022) from Elon Musk, who had received $100 million from the sale of his interest in PayPal two years earlier. Musk became the chairman of the board of directors and the largest shareholder of Tesla.[16][17][14] J. B. Straubel joined Tesla in May 2004 as chief technical officer.[18]
> A lawsuit settlement agreed to by Eberhard and Tesla in September 2009 allows all five – Eberhard, Tarpenning, Wright, Musk, and Straubel – to call themselves co-founders.[19]
* https://en.wikipedia.org/wiki/Tesla,_Inc.#Founding_(2003–200...
He did build the Tesla we know, that is not in question
Others incorporated the company, but he was key to its initial success.