After a renaming of the DocuWare server machine the services do not start.
Within the AuthenticationServer log you can find an error like:

Cannot find active authentication server. All servers are either stopped or the communication channel settings don't allow a connection.
Cannot access server url  'gtcp://DB-VM-2016:9000'. Check that server is accessible and use compatible communication options.
Server identity ComputerID:DB-VM-2016 Domain:QA MachineCredential:MachineCredential:QA/DB-VM-2016 Guid:d99ee86f-9b1d-45f6-8367-4bb276516cdc Type:SettingsServer do not exist

After a server rename no DocuWare services can authenticate against the database.
Depending on the installed service on the server, you can skip to the fitting part for your system

Renamed DocuWare Services
Renamed database
Renamed Fulltext server
All in one
When only the server running the DocuWare Services is renamed, the following steps need to be taken in order to start the services:
Shut down all services via Service Control.
Recreating the system user:
KBA-36437 create dwmachine.config
Use the console commands from the html-file to recreate the systemuser.
You can check the systemuser by opening the dwmachine.config (C:\ProgramData\DocuWare\ServerConfig)

Adjust Authentication Service settings:
Go to your installation path for the AS (Default: C:\Program Files (x86)\DocuWare\Authentication Server)
Open up DWAuthenticationServer.exe.settings with a text editor.
Adjust the server name

Depending on the version, you need to check the other service settings.

Adjust database:
Make sure to have a backup of the database!
Go to dwsystem.dwserver
Adjust the machine_name column to the new Windows server name.
Adjust the connection column to reflect the new Windows server name - be careful about the used ports.

After all changes were made, the services should start again.
You can reset the MSMQ if all services are still offline - KBA-35787

Adjust WebConnection:
Open the Administration.
Switch to "Docuware System - Web Connection".
Alter the machine name if the Web Connection is pointing to this server and not e.g. a LoadBalancer.
If the storage locations or any other network locations are accessed via server name, please check those.
If you renamed your database server, please first follow the documentation of your database to get rid of all issues coming from the database.
This KBA only resolves the issues on DocuWare side of the database usage, for MySQL (internal database), MSSQL and Oracle please consult documentations.

Go to the DocuWare Server.
Use the html from the Setup Components to set the new database server within the dwmachine.config - KBA-36437
Make sure to completely alter the used statement for the correct server, database version, port, user and password.

After this the AS should start and you can open up the Administration.
Now you have to adjust all database connections

If the server running the Fulltext is renamed, you will have to adjust the Fulltext Server Connection.
The Fulltext Server itself has no issues with a change in server names or the like.
If the Index path has the servername as network storage path, this has to be adjusted as well.

If database and all services are located on the same machine, please follow the order below:
Adjust the database settings/connections - see database
After adjusting the dwmachine.config, you have to start with the DocuWare Services
Once the Authentication Server is running, please go back to the database connections - database
As the database connections are all set up, you can finish the DocuWare Service move.
Then finish the move with the Fulltext.