If you read this from the top on down, someone gives an example of what you have to name your shortcut and I believe you need 3 "." after "Delete Conversation"...
One thing I found today which may or may not be helpful to anyone:
And it seems obvious - but - for some reason I didn't have my Messages app set up to use iCloud on my Mac, my iPad, or my iPhone... So every message I was deleting on all 3 devices... Anywhos - I changed my iCloud settings on all 3 devices to enable Messages and now if I delete a message from one device, it is GONE on all 3... Why that is helpful, is that with iPad or iPhone you can select multiple messages and send them to the Trash.... Once done - they are gone forever - even from my Mac Mini.
If you don't have an iPhone or iPad this is of no use to you - but if so - give it a try... It's an acceptable solution for me and was better than creating the shortcut on my Mac which only gave me the ability to CMD-D one message at a time and then manually click on "delete" to boot - so a 2 step process...
I don't know... Worked for me and now I'm slightly less mad at Apple now! :-)