Need IVR Extension in Directory

By default, there doesn’t appear to be a way to add an IVR extension to the company directory. Is there a way to get it in there? 

Here’s my situation: I created a small IVR on extension 44105 for staff to transfer calls into. The IVR lets callers choose between two departments. It works great. However, today the staff manager would like staff to be able to search this IVR by name, rather than enter its number.