Which word should be used to describe this kind of gate [See the picture]?
It is a gate to the yard of the building. (Please correct me if there is a proper way to call the area surrounded by the building.)
Solution 1:
In Scotland such an entrance is termed a pend. It's a useful word that does not seem to have found application the rest of Britain.
"An arch, an archway; an arched or vaulted roof or canopy; the vaulted ground floor of a tower or fortified building; a covered passage or entry; (in later use) especially one leading off a street frontage."
Oxford Lexico
or see Collins