Why might Atwood choose not to reveal the real name of Offred ?
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.
In Margaret Atwood's The Handmaid's Tale, Offred is the name given to the main female character and narrator. Women in the role of Handmaids are given the name "of" followed by the name of the Commander to which they have been assigned. Offred is indoctrinated to the belief that her purpose is merely to serve as a vessel, an empty container, for the purpose of childbirth. Women in her role do not have freedom over their own bodies. The loss of Offred's identity as the woman she once was, lends itself to the reason that her real name is not revealed.
Offred's survival under the new regime requires that she completely conform to the rules given to her by the Aunts in the Red Center. She may be punished or even hanged if she doesn't comply with strict regulations. Offred's real name is a token of something from her past. Her efforts to keep her name to herself serve as a form of self-preservation during a time in which everything else, including her existence, can be taken from her.