The billionaire came up with one idea.
And then another.
But Musk also asked his followers for some suggestions. One user tweeted that it should be called "Tunnel McTunnelFace", to which Musk replied that it had "been done". Another fast-thinking fan said it should be called "Boring Machine", to which Musk (presumably in a sarcastic manner), replied "good one".
The Boring Company is Musk's idea to build a series of tunnels in Los Angeles to travel underground and enable people to avoid traffic. In December 2016, he tweeted that the Los Angeles traffic is driving him "nuts", and then in January of this year, Musk said he plans to start digging in "a month or so".
Musk continued his string of tweets, explaining why he might call it "Ultimate Boring Machine, the Second", rather than "the Third".
The joke presumably refers to his other company Tesla which is gearing up to start the production of its Model 3 car. It's seen as Tesla's first mass market car at $35,000, compared to the company's other higher-priced vehicles – the Model S and Model X.
But there appears to be confusion over the naming of the cars, with some consumers thinking that the Model 3 is the next version of the Model S, something that Musk addressed recently.
"We have seen a belief among some that Model 3 is the newest and more advanced generation of Model S. This is not correct," Musk wrote in a letter to shareholders earlier this week when Tesla released its first-quarter earnings.
"Model S will always have more range, more acceleration, more power, more passenger cargo room, more displays (two), and more customization choices, and Model S, X and 3 will all have equivalent Autopilot functionality. We will continue to clearly communicate these distinctions to avoid any misperceptions."
Last week, The Boring Company released a video showing what the underground system would look like. And pictures have surfaced on social media that claim to show what the tunneling machine would look like.