The name of Apple's file management app on iOS is Files.
Apple introduced Files with iOS 11 in 2017, replacing the standalone iCloud Drive app as the main place to browse and organize documents. It lets users view files stored locally and in services such as iCloud Drive, Dropbox, Google Drive, OneDrive, and Box.
Files supports folders, subfolders, tags, sorting, search, renaming, moving, sharing, and deleting. On compatible devices, it can also work with external storage and compress or extract ZIP archives. iPad users can drag files between Files and other apps.
A common mix-up is Finder, which is Apple's file browser on macOS. “File Manager” and “Documents” are generic or third-party names, not the official name of Apple's built-in iPhone and iPad app.