On a fresh install, TEI Publisher creates a user tei with a password simple. It also creates another user tei-demo with a password demo, who can upload documents into the Playground collection. You can change these passwords (and it is strongly recommended to do so, if your eXist instance runs on a server and would be accessible to other users).
When generating your own application, the generator form requires you to fill in a user and password for the new application. Likewise, this password can be later changed via eXist Usermanager.