What is the name for the opening in the mouth for the nasal passages?
From what I understand from your comment is that you are asking for opening which connects the nasopharynx to oropharynx.

This opening is is connecting two parts of pharynx , acting like a bridge therefore it was named as Pharyngeal/Nasopharyngeal isthmus.

According to this site:


  isthmus of pharynx
  
  Type:Term
  
  Definitions
  1. passage posterior to the soft palate by which the nasopharynx and oropharynx communicate (i.e., the junction of nasopharynx and oropharynx), closed during swallowing by elevation of the soft palate and contraction of the posterior fascicle of palatopharyngeus (muscle), forming a Passavant cushion.
  
  Synonyms 
  isthmus pharyngis , pharyngeal isthmus






Source of image: Textbook of Anatomy: Head, Neck, and Brain : Vishram Singh