You either mean an Arbor or a Pergola... pergolas are usually attached to the house, but you can also build them free-standing.
path
The name of a covered walkway that surrounds a courtyard is a cloister.
Arcade
An old covered walkway is called a stoa from Greek architecture.
I warily weaved my way across the windy elevated walkway. The walkway through the garden was choked with an abundance of overgrowth.
stoa
17000
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A promenade?
pergola
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