Discourse admins can disable the ability to initiate personal messages for users globally using the personal_message_enabled_groups site setting.
Note that with this setting even if a user cannot initiate personal messages, they are still allowed to reply to existing messages.
Additionally, admins and moderators always retain the ability to create personal messages with any user, regardless of the personal_message_enabled_groups settings.
Individual users can also adjust if they want to be able to receive personal messages on their Preferences -> Users page under the Messages section, and can choose the option to allow/disallow other users to send them personal messages and chat direct messages, and (optionally) to only allow specific users to send them personal messages or chat direct messages.
