In World of Warcraft: Forever every character has two names instead of a single name tied to a realm. Together they form the full name, which must be unique within a region.
Early Name Reservation runs from October 27 through November 3, 2026 for eligible upgrade purchases. Names are reserved on a first-come, first-served basis. The source is the Wowhead report, checked against the Blizzard original: https://worldofwarcraft.blizzard.com/en-us/news/24304161/create-a-name-of-your-own-in-wow-forever
Unique across a region
What counts is the complete combination of both names. Two characters may share the same first name as long as the full names differ. Uniqueness is required across the whole region, not per realm.
Naming rules still apply: certain names, words, spellings and repeated-character patterns can be restricted, for example confusing ones or ones impersonating Blizzard. Both parts are evaluated together, so splitting a restricted word across the two names does not necessarily make it valid. If your desired name is taken or not allowed, pick another combination or use the random name generator.
Hiding the secondary name
If you prefer a simpler look, you can hide the secondary name in the game world: Game Menu (Esc), Options, Nameplates, tick "My Secondary Name". The secondary name still appears in chat.
Original report: Wowhead