Can my dedicated number receive SMS from a business name sender ID?
No. A message sent from a business name sender ID (a sender that shows a company or product name instead of a phone number) is blocked and never reaches your account. It won't appear in Messenger or trigger your automations. This only applies to business name sender IDs. Messages from a phone number aren't affected by it.
If the service sending you these messages can send them by email instead, Email to SMS can turn each email into an SMS to you or your team.