Final answer:
A private or side entrance next to a porte cachère is known as a vestibule, which is a small entrance hall or anteroom leading into the main part of a building.
Step-by-step explanation:
A private or side entrance called as one for pedestrians next to a porte cochère is known as a vestibule. This term refers to a small entrance hall or anteroom leading into the main body of a building. Examples of vestibules can be found across various architectural designs, such as the entryway into historical houses, churches, or mosques. For instance, in Roman architecture, the fauces or vestibulum served as the entryway into a typical atrium house. The term atrium refers to an open-air central hall in ancient Roman houses, not to be confused with a vestibule. Similarly, the term portico describes a roofed space, open or partly enclosed by columns, leading to the entrance of a building, like the grand entrance to Diocletian's private apartments. Therefore, among the choices given, a vestibule is the correct term for a private or side entrance next to a porte cachère.