A kerbonaut is the KSP equivalent of an astronaut. Kerbonauts are the select Kerbals who crew vehicles launched from Kerbal Space Center. They wear an IVA suit and helmet inside of crafts, and an EVA suit and helmet outside. The EVA suit includes helmet lights and a jetpack meant for maneuvering in outer space.
Each kerbonaut has two personality attributes – Courage and Stupidity – which are displayed in-game. There's a small chance they may also have the hidden "BadS" attribute. These attributes together affect how a kerbonaut reacts to decouplers decoupling, vessels accelerating, and other variously lethal events.
Every game starts with the same "original three" kerbonauts hired and ready. More can be hired in the Astronaut Complex, each one having random amounts of Courage and Stupidity and a (rather) small chance to have the BadS stat enabled. Each kerbonaut also has a random first name; the surname of any kerbonaut, and of all known Kerbals, is always "Kerman".
The Original Three
Every new game, whether Sandbox or Career mode, begins with three kerbonauts already on the roster. While all other kerbonauts have randomly generated names and stats, these three are always the same. Their names are Jebediah Kerman, Bill Kerman, and Bob Kerman.
These are the only “veteran” kerbonauts in Kerbal Space Program, designated by orange IVA suits and icons in crew interfaces; everything else is visually identical to all kerbonauts. In some of the game's loading screens, three orange suited kerbonauts (presumably Jeb, Bill, and Bob) have helmets with orange stripes though no such helmet is seen in-game – IVA helmets have grey stripes and EVA have red.
Their presence at the top of the list of kerbonauts in every game means they each have much greater likelihood of being aboard any given vessel than does any random kerbonaut, with Jeb being far and away the most likely to pilot any craft any time he's available. This, and their presence in every player's games, makes them the most famous faces of KSP.
The term kerbonaut seems to be an invention of KSP fans. The in-game building for hiring crew is named the Astronaut Complex after all. As the developers at Squad are the authors of the Kerbal universe, it makes sense to consider their terms official.
However, fans persist in “adding K to every word” as evidenced by mods like the Kerbonaut Creator, use in KSP fan fiction, forum posts requesting kerbonaut veteran suit colors, etc. If notoriety in another huge indie game is any barometer, there are about 12x more views of a Kerbonaut Minecraft skin than a Kerbal astronaut Minecraft skin on the same site.
In real-life, “astronaut” is not a universal term; it principally refers to NASA and sometimes European Space Agency explorers. The term “cosmonaut” (Russian: космонавт) has been used since Soviet times and could make a historical case for being the first choice. Eastern European and former Soviet bloc countries have invented terms based on the Russian, while other nations have used other terms based on ”astronaut”. In modern times, Chinese sources use either term depending on the audience they're speaking to, though ”háng tiān yuán” represents their native term for space travellers other than China's. Meanwhile, western media invented the term ”taikonaut” for China's space travellers.
If there is a universal trend, it seems that terms for "people who go to space" get tied in with national identities. However, KSC and characters like Wernher von Kerman and Gene Kerman more closely resemble the US space program of the 1960s than any other space program. In the end, it's hard to say what should be said.