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.
What is also interesting is part of the act is pretending he is the genius behind the ideas and has a hand in the novel engineering of them, which makes some of his fans love him, and anyone with subject matter expertise on whatever technical things he's saying realise he's half a moron or at least shameless.
Even if these insights into specific industries aren't his own, he's savvy enough to recognize their validity and bring together other people who can make those insights reality.
At the same time, he has his fair share of boneheaded boondoggles.
Musk has always been brutally transparent with investors. The personal genius schtick isn't one he pulls when raising capital. (It does play well to a lay audience.)
History is littered with entrepreneurs and inventors who lost thier marbles.
Howard Hughes is way more famous for the spruce goose and being a hypochondriac shut in with the general public than anything else!