Anthem has religious denotations as a choral work or part of a prayer service, although a more prevalent usage of the word finds it in combination with the word national. The national anthem of a country, then, is a celebratory song that elicits pride and loyalty in those who sing it. These two definitions of anthem, as a religious song and a celebratory song, are both appropriate to the novel by Ayn Rand. 

In the final chapters of Rand's novel, Equality is banished into the wilderness, but Golden One later follows him because she loves him. At first, they cannot express this love since they have no word for it. However, after Equality discovers some books and he begins reading, he is able to articulate some of his feelings. Further, he discovers the word I. Near the end of Chapter 11, he writes,

I am a man. This miracle of me is mine to own and keep, and mine to guard.
I am done with the monster of "we," the word of serfdom...of falsehood and shame.
And now I see the face of god, and I raise this god over the earth...this god who will grant...joy and peace and pride.

In Chapter 12, Equality writes that on the mountain his sons and he, along with his chosen friends, will build their new land. Then, Equality, who has given himself the name Prometheus, clearly writes an anthem himself, one that can be sung with both religious fervor and celebration:

For the coming of that day I shall fight, I and my sons and my chosen friends. For the freedom of man. For his rights. For his life. For his honor.

This, indeed, is the anthem he has sought. This is the anthem, too, for which he has fought and will now live.

The Ayn Rand Institute's Centennial Edition of Anthem has an Introduction preceding the novel that explains this exact issue. At first, Rand's working title for the book was "Ego" because her philosophy centers around individualism and the strict meaning of this word--"self." Rand seemed to use a working title as she penned the work so to keep her centralized on her purpose for writing. Later, and for publication purposes, she would change the titles in order to spark readers' interest in the book. It is also said that her working titles were unemotional, again, in order to keep her writer's focus on the purpose of the text. The publication title should invoke interest for the reader and allow the reader to investigate as to how the title was chosen for the book. If one looks up the word "anthem" in the dictionary, it says that an anthem is a song of celebration or praise, as well as a being held sacred. For Rand, the individual is the most sacred and must be defended against all collectivism.