The Black Kogatana is an item that can hold the power of an individual Persona inside of it. This is done through fusion in the Velvet Room. However, it will not be immediately available, so if you acquire the Black Kogatana (or the Black Rock or Model Gun) earlier in the game, do not sell them, and progress through the story further.
A sword that possesses the power to transmutate
Once Igor grants you the ability to itemize Personas, you be able to use these items as fusion material alongside your favorite Persona. When combined, they will create powerful and unique weapons for you to use.
Your best bet for farming these transformation items is to head to Mementos. Here, you will be able to acquire them by random chance just by clearing out the floors. Make sure to check regularly at the thrift store by Leblanc, as the old man there will occasionally have these to sell. They are also located in some palace chests, but as these are very story dependent moments that last only for a small time, Mementos and thrift shop hunting will be a far more reliable method.
If you put in the time to acquire these items, as well as progress far enough to get the ability to itemize Personas, you will be able to build some of the most powerful weapons in the game for you and your teammates.