Why was it called Kiryat Arba?

Summary: I believe that what drives Rashi is first peshat and second derash. But there are complications, in the form of an explicit pasuk which seems to contradict Rashi's peshat.

Post: Sarah dies in Kiryat Arba, which is Chevron. The pasuk, with Rashi's comment:

2. And Sarah died in Kiriath arba, which is Hebron, in the land of Canaan, and Abraham came to eulogize Sarah and to bewail her.		ב. וַתָּמָת שָׂרָה בְּקִרְיַת אַרְבַּע הִוא חֶבְרוֹן בְּאֶרֶץ כְּנָעַן וַיָּבֹא אַבְרָהָם לִסְפֹּד לְשָׂרָה וְלִבְכֹּתָהּ:
in Kiriath-arba: lit. the city of the four. So named because of the four giants who were there: Ahiman, Sheshai, Talmai, and their father (Gen. Rabbah from Num. 13:23). Another explanation: Because of the four couples that were buried there, man and wife: Adam and Eve, Abraham and Sarah, Isaac and Rebecca, Jacob and Leah (Pirkei d’Rabbi Eliezer , ch. 20).		בקרית ארבע: על שם ארבע ענקים שהיו שם אחימן ששי ותלמי ואביהם. דבר אחר על שם ארבעה זוגות שנקברו שם איש ואשתו אדם וחוה, אברהם ושרה, יצחק ורבקה, יעקב ולאה:

Thus, Rashi gives two explanations, both drawn from midrash. But the first one is quite similar to a pasuk in sefer Yehoshua, as well as a pasuk in sefer Bamidbar, which appears to attribute the etymology of Kiryat Arba to the four giants who lived there. Therefore, I would take this first explanation as his peshat explanation. The second explanation does not accord with any explicit pasuk, but it fits well into the theme of this parsha and the use the Mearat Hamachpela is to be put to. After all, Avraham here buys the field and cave as an achuzat kever. That, I would say, is why Rashi selects this particular midrash from the midrashim he could have selected from.

Note that while Judaica Press, in translating Rashi, attribute the midrash to Pirkei deRabbi Eliezer -- and they are correct -- there is sufficient material in Midrash Rabba for this as well. For Bereishit Rabbi gives several explanations:

ותמת שרה בקרית ארבע ארבעה שמות נקראו לה:
אשכול,
וממרא,
קרית ארבע,
חברון.
ולמה הוא קורא אותה קרית ארבע? שדרו בה ארבעה צדיקים:
ענר,
אשכול,
וממרא,
אברהם.
ונמולו בה ארבעה צדיקים:
אברהם,
ענר,
אשכול,
וממרא.
דבר אחר: קרית ארבע שנקברו בה ארבעה צדיקים אבות העולם:
אדם הראשון,
אברהם,
יצחק,
ויעקב.
דבר אחר: שנקברו בה ארבע אמהות:
חוה,
ושרה,
ורבקה,
ולאה, 
ועל שם בעליה שהן ד' ענק וג' בניו.

אמר רבי עזריה:
שמשם יצא אבינו אברהם, שרדף אחרי ארבע מלכויות קוזמוקרטורין.

דבר אחר:שהוא עולה בקרנסין של ארבעה.
בתחלה ליהודה,
ואחר כך לכלב, ואח"כ ללוים,
ואחר כך לכהנים. 

I suppose the combination of the patriarchs with the matriarchs into pairs is unique to Pirkei DeRabbi Eliezer. Regardless, there was what to select from, and Rashi chose these two.

Focusing now on the first explanation, that it was named after the four giants who lived there, this finds explicit Scriptural basis in Bemidbar 13:22, that giants lived there:

22. They went up in, the south, and he came to Hebron, and there were Ahiman, Sheshai, and Talmai, the descendants of the giant. Now Hebron had been built seven years before Zoan of Egypt.

כב. וַיַּעֲלוּ בַנֶּגֶב וַיָּבֹא עַד חֶבְרוֹן וְשָׁם אֲחִימַן שֵׁשַׁי וְתַלְמַי יְלִידֵי הָעֲנָק וְחֶבְרוֹן שֶׁבַע שָׁנִים נִבְנְתָה לִפְנֵי צֹעַן מִצְרָיִם:

In terms of translating הָעֲנָק, I am not sure that it means a particular giant. It seems to be more of a collective noun, in context. Thus, these were descendants of giants. The sum of giants would then be three, rather than four. But if it were a particular giant, their father, then the sum would be three. Compare the pasuk later in the same perek:

33. There we saw the giants, the sons of Anak, descended from the giants. In our eyes, we seemed like grasshoppers, and so we were in their eyes.

לג. וְשָׁם רָאִינוּ אֶת הַנְּפִילִים בְּנֵי עֲנָק מִן הַנְּפִלִים וַנְּהִי בְעֵינֵינוּ כַּחֲגָבִים וְכֵן הָיִינוּ בְּעֵינֵיהֶם:

which I believe bolsters the idea of anak being collective rather than particular.

There is also Scriptural basis, I believe, for treating Arba not as a personal name but as a thing -- perhaps a number. Thus, in these two pesukim:

בראשית פרק לה

• פסוק כ"ז: וַיָּבֹא יַעֲקֹב אֶל-יִצְחָק אָבִיו, מַמְרֵא קִרְיַת הָאַרְבַּע--הִוא חֶבְרוֹן, אֲשֶׁר-גָּר-שָׁם אַבְרָהָם וְיִצְחָק. 

נחמיה פרק יא

• פסוק כ"ה: וְאֶל-הַחֲצֵרִים, בִּשְׂדֹתָם--מִבְּנֵי יְהוּדָה, יָשְׁבוּ בְּקִרְיַת הָאַרְבַּע וּבְנֹתֶיהָ, וּבְדִיבֹן וּבְנֹתֶיהָ, וּבִיקַּבְצְאֵל וַחֲצֵרֶיהָ. 

note how it is Kiryat ha-Arba. The definite article does not go on proper nouns. We would never say ha-Moshe, for example. This might well be a cue for Rashi, and the midrashim he is basing himself on, to say that it refers to four, rather than, say, an individual whose name was Arba.

There is one problematic pasuk which appears to give an etymology to the place name, though one at odds with all this. In sefer Yehoshua, 14:15:

יהושוע פרק יד

• פסוק ט"ו: וְשֵׁם חֶבְרוֹן לְפָנִים קִרְיַת אַרְבַּע, הָאָדָם הַגָּדוֹל בָּעֲנָקִים הוּא; וְהָאָרֶץ שָׁקְטָה, מִמִּלְחָמָה.  {פ}

Judaica Press' translation, coupled with Rashi's commentary:

{Arba} was the greatest man among the Anakim: Arba was the name of the father of Ahiman, Sheshai and Talmai. Another explanation is: [It was called Kirjath-arba, the city of four] because of the father and the three sons for the scripture calls them the children of 'Anak.

I put Arba in {curly brackets} since it is not explicitly part of the pasuk. As I see it, Rashi here is grappling with this issue. Not just midrash vs. explicit pasuk, but perhaps even the definite article issue I mentioned coupled with that pasuk in Bemidbar which indicated three others.

Therefore, I would guess that in his two interpretations in sefer Yehoshua, he is not merely opposing the explicit pasuk to the midrash, but reading both into the pasuk. In the first interpretation, Arba is the name of the person, who was the father of the ones we saw in Bemidbar. Thus, Arba is the anak, the giant, and the city was named after him personally. In the second explanation, it is not clear that Arba was necessarily the name of the giant. Rather it was because now they number four. I must say, how this would fit into the word of the pasuk is still a bit unclear to me, and it seems more than a bit awkward. Perhaps take הוא as if it said הם?

(See what other meforshim have to say about this etymology.)

Regardless, it is this second interpretation in sefer Yehoshua which he gives as his first (peshat-oriented) explanation in our parasha of Chayei Sarah.

After writing this, I thought to look to Aharon ben Yosef the Karaite. As a Karaite, he has no reason to favor the midrash. And, at the same time, he is concerned with dikduk and thus would note the definite article in kiryat ha-Arba. This would then be a good gauge for whether Rashi is saying peshat (as I believe) or derash.

And indeed, Aharon ben Yosef the Karaite agrees! I'll cite him local to Chayei Sarah and local to sefer Yehoshua.

In Chayei Sarah:

In sefer Yehoshua:

I confess I am not absolutely sure what he means. I mean, in Chayei Sarah, he seems to initially designate it as a person's name, but then notes the heh of the definite article, which means that it could not be a personal name. Therefore, Arba (or ha-Arba) is a designation, though not a proper name, for him and his three sons. So, in the end, I take it that it means "four", and that it could also refer to the individual, the father of the other three, because of this.

In sefer Yehoshua, when he transitions to נקרא כן, does that refer to the city or the man? Whichever, "it" is called that because of him and because of his three sons. This strongly echoes Rashi's second peshat in sefer Yehoshua, that it was על שם האב וג' בנים שכן קורא אותם ילידי הענק.

Thus, due to the definite article, this Karaite scholar agrees with Rashi.

BTW, here are Mizrachi and Gur Aryeh on the matter.