What is the name of Pokémon's in-game encyclopedia?

Pokémon's in-game encyclopedia is called the Pokédex.

The Pokédex records information about Pokémon species encountered or caught by a Trainer. In the original games, Professor Oak gives the player a Pokédex and asks them to document the species found in the Kanto region.

Its name combines “Pokémon” with “index,” reflecting its cataloging function. The device appears in games, anime episodes, manga, and other Pokémon media, although its appearance and capabilities vary between regions and stories.

The Pokédex is not the same as the PokéNav, Pokégear, or other regional devices. Those tools provide navigation, communication, or additional gameplay features. The Pokédex's defining purpose is identifying and cataloging Pokémon species.