Is there a term or phrase for a list of residents displayed at the door in a shared home?

directory

The rugged stainless steel faceplate has a printed name directory housed in a waterproof, scratch-resistant lens. Each button is beside the tenant's name in the apartment directory.

https://www.vikingelectronics.com/products/k-1200/

This name directory is designed specifically to complement secure building door entry systems and is constructed for both weather and vandal resistance.

https://www.vikingelectronics.com/products/d10/

Edit to add: the USPS guidance refers to directory:

632.626 Directories

Guidelines for Postal Service apartment house directories are as follows:

a. For all apartment houses with 15 or more receptacles, maintain a complete directory of all persons receiving mail. If an apartment house is divided into units, each with separate entrances and 15 or more receptacles, each unit should have a separate directory. In addition, if mail is not generally addressed to specific units, a directory must be kept at the main unit of the building listing all persons receiving mail in the various units.

Directories must be alphabetical by surname and must be maintained and kept up-to-date. ...

c. The directory must be legible, enclosed in a suitable protective frame, and attached to the wall immediately above or to the side of the mail receptacles where it can easily be read.

https://about.usps.com/what-we-are-doing/current-initiatives/delivery-growth-management/section-632.pdf