Does the appositive in this sentence need to be set off with commas?

On the freelancing website Upwork, there is a US Punctuation and Mechanics test one can take to boost credibility on one's profile for potential clients. These tests are administered by third-party companies that often hire non-native English speakers, so they're known to have some inaccuracies. Unfortunately, because you're allowed to retake the exams after a certain period passes, the correct answers are never revealed.

One of the questions on this exam is the following:

Richard’s wife(A) Abigail(B) is an incredibly talented cook(C) and gardener.

Comma at (A)

Comma at (B)

Comma at (C)

Comma at (A) and (B)

No commas needed

I answered "No commas needed", but I suspected afterwards that the answer key was looking for the answer choice above it, "Comma at (A) and (B)". After searching this question online, I found a website with answers for the various questions on the test, and the site claims that "Comma at (A) and (B)" is in fact the correct answer for this particular question.

Is the answer key wrong? I feel like there's really no need for any commas, but on the other hand, the appositive Abigail isn't restrictive because it doesn't offer terribly "essential" information, suggesting it could be set off by commas.

Commas are used to set off an appositive when the appositive can only refer to a specific item. (The Chicago Manual of Style, 5:21,123; 6:22-24)

Examples:

Mary's son, Jesus, is thought by many to be the Messiah.

Dostoevsky's book Crime and Punishment is considered one of the great books of all time. [Dostoevsky wrote more than one book]

My only brother, Scott, is a great dude.

My brother Scott is one of eight boys in my family.

My favorite newspaper, the Chicago Tribune, is going downhill in a big way.

The magazine Newsweek is going downhill in a big way. [There are many magazines, perhaps others going downhill as well.]

So let's look at your example:

Richard's wife (A) Abigail (B) is an incredibly talented cook (C) and gardener.

1. Commas are used at A and B because Richard has only one wife. I suppose you could argue there are still places on earth where men can be polygamous .. but it would be a weak argument.

2. Item C does not have a comma because two objects do not make a series. Serial commas require at least three items. Such as: Richard's wife, Abigail, is a talented cook, gardener, and lover.

You're right. But so is the answer key.

I don't quite agree with the answer key, I do think that no commas would have been equally correct. However, I do see what the answer key is trying to argue.

Consider the following two sentences:

1. My brother, who is a physician, has died yesterday.
2. My brother who is a physician has died yesterday.

1. states that I only have one brother, who also happens to be a physician.

2. allows for the possibility that I have many brothers, but I am currently talking about one specific brother (the one who is a physician). This implies that I have only one brother who is a physician, but I could have other brothers (who are not physicians).

Richard’s wife Abigail is an incredibly talented cook and gardener.

The answer key is arguing that because someone can only have one wife (due to polygamy being illegal), there is no need to add "Abigail" as way to further distinguish which wife we are talking about.
I refer back to my earlier example. You would expect example 1. to be used, because there is only one brother/wife. Therefore, her name is tangential information, not a necessary distinction.

While that is correct, I do think that it is overly pedantic.

1. Polygamy is allowed in some cultures. If Richard is a Mormon (who allow polygamy, even if they can't legally enforce that. There are cases of polygamy being legal) it does need to be specified.
2. If we change the sentence to "Richard’s ex-wife Abigail", then the distinction does become important, as you can have more than one ex-wife.
3. If Richard has been married multiple times, and you are talking about a past event, then it is relevant to mention which wife you are talking about (if it was not already clear from the context)

The answer key is relying on the local culture (polygamy being illegal) to argue its grammatical correctness. As this is a test designed to test your grammar skills, not your knowledge of legislature, the answer key completely misses the point of the test.

The answer key is not wrong to say that "Comma at (A) and (B)" is correct. It is indeed correct.

However, the answer key is wrong when it says that your answer ("no commas needed") is wrong, because it can be equally correct.
And in my opinion, you are more correct because your answer applies regardless of the specific context or words used, which is the goal of the test.

If you observe the local cultural context, you can argue that your answer is creating an unnecessary distinction, but that does not make it wrong.