Bates numbering is a specific legal convention, and getting it right matters because the numbers become the shared reference for every document in the matter, so the definition first then the tooling:

What it is: a unique sequential identifier stamped on every page across an entire document set, typically a prefix plus a zero padded number, ABC000001, ABC000002, continuing unbroken across all documents so page ABC000342 refers to exactly one page in the whole production forever. The prefix identifies the producing party or matter, the padding keeps them sorting correctly and the continuity across files is the essential property, since the whole point is a stable citation everyone uses.

What applies it: Adobe Acrobat has a dedicated Bates Numbering feature, Tools, Edit PDF or the older Document menu depending on version, Bates Numbering, Add, which takes a set of files, applies the prefix, starting number and padding and stamps them continuously across the whole set in one operation, the built for purpose tool most legal work uses. It records the range so you know the set runs ABC000001 to ABC004237.

The alternatives: dedicated legal document tools and e-discovery platforms Bates stamp as core functionality with more control, and for smaller matters PDF tools with a Bates or sequential stamp feature plus scripts using pypdf can do it, though the legal specific tools handle the conventions, endorsements, confidentiality stamps alongside the Bates number, that matters real work expects.

The disciplines that keep a Bates set valid: number the final version of the set, since renumbering after adding documents breaks every citation already made, choose a prefix and padding wide enough for the whole matter's eventual size, and keep a record of what range covers what, the load file or index that maps Bates ranges to documents. Bates numbering done once correctly is a matter's backbone, done carelessly it is a source of citation chaos, which is why the legal specific tooling earns its place over generic page numbering.