VDA might turn to "Unregistered" state when 'BrowserName' property of published application contains special characters, e.g. a pair of brackets.

Remove the special characters (e.g. brackets) from 'BrowserName' property by Set-BrokerApplication posh command.
For example, 

• $app = Get-BrokerApplication -PublishedName "OriginalName"
• Set-BrokerApplication -InputObject $app -BrowserName "NewName"

Problem Cause

For published application, the following special characters are actually not allowed in the Name, BrowserName or the PublishedName properties: \ / ; : # . * ? = < > | [ ] ( ) “ ‘, regardless of in half-width or full-width. While New-BrokerApplication command-line or Studio may wrongly accept those special characters in full-width as a part of Name, BrowserName and PublishedName properties.

When 'BrowserName' property of a published application contains the mentioned special characters, upon the VDA registration (who hosts the published application), DDC side UpdateWorkerSessions procedure may run into “Cannot insert duplicate key in object 'dbo.@InstancesByBrowserName'" exception and eventually result in the registration failure.

https://developer-docs.citrix.com/en-us/citrix-virtual-apps-desktops-sdk/2402/Broker/New-BrokerApplication.html