A promenade?
The name of a covered walkway that surrounds a courtyard is a cloister.
path
An old covered walkway is called a stoa from Greek architecture.
stoa
pergola
You either mean an Arbor or a Pergola... pergolas are usually attached to the house, but you can also build them free-standing.
A covered walkway is basically like an outdoor tunnel, which is designed to keep employees and public in a dry and wind free environment. Find out more by visiting the site in the related links.
une allée couverte
That would be a "walkway" or a "tunnel".
a walkway
Path or footpath are two other names for a walkway. Causeway, alley, catwalk, passageway, and passage are other names for a walkway.