The reader is introduced to THT's patronymic naming system via "newness" in the SF-specific, Huntingtonian sense. In the first section, we are clued in to the fact that something is awry in the book's world, naming-wise, by the sort of ominous catalogue of pedestrian Catholic school-girl-sounding names: "Alma. Janine. Dolores. Moira. June" (4). ("Aunt" seems like a strange title, too, but there are other things to worry about for the moment.) This is then followed by the introduction of Rita the Martha.: "Rita is in here, standing at the kitchen table, which has a top of chipped white enamel. She's in her usual Martha's dress…. She puts on the veil to go outside, but nobody much cares who sees the face of a Martha" (9). Here, we find a recognizable use of naming paired with an unrecognizable use of naming, so that we know that certain names are used in the same way in this world as they are in our world, and certain names are used very differently. What, we wonder, is a Martha?
In the same chapter, we're introduced to Serena Joy, the Commander's Wife. At this point in the novel, it seems pretty clear that the improbable name "Serena Joy" is a stage name from "The Growing Souls Gospel Hour" (16). In the rest of the novel, though, she still bears the same name, and there is never any attempt to delve into the matter further.
Then, finally, amid this small amount of name-related confusion, we get introduced to the patronymic naming system: "Her name is Ofglen, and that's about all I know about her" (19). This is sort of a tricky way for Atwood to have gone about this business, since "Ofglen" is less immediately transparent than, say, "Ofcharles" or even "Ofwayne"--it is more than possible, that is, to look at the word "Ofglen" and see only a weird, quasi-Nordic name, without yet discerning the system and its purpose. It is also important, I think, that Ofglen's name is presented as an absolute fact--"that's about all I know about her." Ultimately, it will become clear that to give "Ofglen" as Ofglen's name is to give a sort of misinformation. She surely does have another, real name. It's simply the case that the narrator isn't privy to this information. But--strangely, I think--she doesn't seem concerned by this.
The scene in the Milk and Honey store is the first time that real information about how naming is worked gets revealed to the reader. This makes a certain amount of sense, since this is also the first instance of significant social interaction. First, there's the revelation that places can't really conceivably be named in words but must instead be named with pictures--"Our first stop is at a store with another wooden sign: three eggs, a bee, a cow. Milk and Honey" (25). The naming of women gets revealed in a way that looks incidental--via gossip: "'Who is it?' I hear behind me. 'Ofwayne. No. Ofwarren'" (26). It takes the juxtaposition of these two names--in conjunction with the already-given "Ofglen"--to solidify our understanding of what's going on as far as women's names. This is exactly the sort of principle of "newness" that Huntington points out as in Neuromancer. First, the reader is introduced into a system that feels somehow foreign or different but that is not explained in detail. It works sort of like Kafka, in a way--we just have to accept the information given to us. But, unlike in Kafka, things eventually get explained, get reordered into a system that, while still unfamiliar, seems at least logical.
I think what remains sort of disturbing or sinister about naming in The Handmaid's Tale is that none of it is ever fully explained. The new system is never fully revealed. We never know, for instance, what Offred's "real" name was. (And even her patronymic seems hopelessly vague: just as "Ofglen" looks in a certain sense opaque to me, I can't look at "Offred" and not read "Off-red," as in the color--the color of the handmaids' dresses, perhaps?)
Even the "Historical Notes" section seems perplexed by the amount of information we get: "She does not see fit to supply us with her original name…. The other names in the document are equally useless for the purposes of identification and authentication. 'Luke' and 'Nick' drew blanks, as did 'Moira' and 'Janine.' There is a high probability that these were, in any case, pseudonyms" (306). Far from comforting or explanatory, the historical notes further undermine whatever sense of confidence or normality we might have found in, e.g., Moira's name.