No, Mastodon is not a public company.
You cannot buy shares in Mastodon, however you can contribute to the growth of Mastodon by hosting new Mastodon instances (domains on the Mastodon network).
People who use the platform contribute to its development, meaning that it’s not owned by a single entity nor by shareholders.
This is key to the vision of Mastodon which is intended to democratize social media rather than all users being at the whim of one owner (à la Mark Zuckerberg or Elon Musk).
Who Owns Mastodon?
As a decentralized open-source platform Mastodon is owned by its users and those who create servers to host new Mastodon instances on.
However it was founded by Eugen Rochko.
Eugen Rochko was born in Russia in 1993 and moved to Germany in 2004 at the age of 11, he started working on making Mastodon a reality in 2016 having become disillusioned with the state of social media and wanting to create a democratized social media platform.
How Mastodon Makes Money
Despite not being a public company Mastodon does need to make money to cover costs for staffing, hosting and resources.
It does this in a number of ways: