As Kaste has said, the name comes from the empire’s founder, Osman Bey. But how did “Osman” get to “Ottoman”, you ask? It’s a weird story, actually. Just promise me you won’t go to sleep.
There are many theories as to why, and all of them are quite boring. Basically, it was because of semantics. Some argue that Osman’s original name was “Ataman” or “Atman”, and that it changed to Osman, a name of Arabic origin, later on. However, early Byzantine sources, such as that of George Pachymeres, refer to him as “Atouman”, which would explain why we call his descendants the Ottomans. It likely came about because of the way way how Greek sources recorded his name. You have to remember that the term “Ottoman Empire” was used by foreigners. The actual Ottomans wouldn’t have called their state that.
Wikipedia even has a small section on his name in their article about Osman Bey.