The word "calligraphy" is a noun. In the sentences you provided, it functions as the subject and represents the art of producing beautiful writing with a special pen or brush.
The art of producing beautiful writing with a (special) pen or brush is called calligraphy.
Subject: "The art of producing beautiful writing with a (special) pen or brush"
Verb: "is called"
Object/Noun: "calligraphy"
In this sentence, "calligraphy" is a noun that represents the art form of producing beautiful writing using a special pen or brush. It is the object of the verb "is called," indicating the name or label for the described art.