The Handmaid's Tale by Margaret Atwood is a dystopian futuristic novel in which Atwood critiques what she sees as many of the alarmingly regressive and patriarchal attitudes found in the United States, especially with regard to limiting women's freedoms to control their own bodies. In the society of the novel, women have no freedom at all, and are confined to limited reproductive and sexual roles.
Part of the system of oppression in the theocratic Republic of Gilead involves subjugating people by breaking down the identities that define them as people. Thus the subordinate status of handmaids in the novel is emphasized by their being deprived of their names and only known by the names of the men to whom they are given. The only way for Offred to reclaim her real name would be to succeed in escaping to Canada and reclaiming her identity.
The namelessness of Offred also is a comment on how patriarchal history has tended to forget the names of women.