How to create an SPN for an ADFS server with an alias

I have a colleague who has set up an ADFS server in a test environment and that have given the ADFS server an alias.

host name test-server.tdom.com
alias test-adfs.tdom.com

The server is running under a specific AD user account.

The replying party trusts have been set up to trust the alias.

We have been able to set SPNs for the host name as follows

setspn -s HTTP/test-server.tdom.com Admin
setspn -s HTTP/test-server $

But not for the alias if he tries to register.

setspn -s HTTP/test-adf $ returns a message stating the "account test-adf $ cannot be found".

Congruently we cannot get IWA to function.

Does anyone know how the SPN can be set for the alias.