No officially recognized constellation has a name that starts with the letter K. The International Astronomical Union keeps a fixed list of 88 constellations, and not a single one of them begins with K. This is a small surprise for many sky watchers, because the night sky holds famous patterns for almost every other letter, yet K is simply left out of the catalog.
The reason comes down to history and language. Most constellation names trace back to ancient Greek and Latin, and these names were later standardized into Latin spellings when astronomers built the modern list. Latin rarely uses the letter K, since the same hard sound is usually written with a C instead. Because of this spelling rule, names that might have started with a K sound were recorded with a C, which removes the letter K from the official roster entirely.
A few familiar stars and patterns come close enough to cause confusion. Many people think of the bright star Kochab, which sits in the constellation Ursa Minor, or the well-known star Capella, whose hard C sound feels like a K. There is also the constellation Carina, the keel of the ancient ship Argo, which carries the meaning of a keel even though it is spelled with a C. These examples show why the K sound feels present in the sky, even though no constellation name actually begins with the letter K.