The phrase appears not only in Gen 31:42:
MT ... אֱלֹהֵי אָבִי אֱלֹהֵי אַבְרָהָם וּפַחַד יִצְחָק ...
= ... ʾĕlōhê ʾābî ʾĕlōhê ʾābrāhām ûpaḥad yiṣḥāq ...
LXX ... ὁ θεὸς τοῦ πατρός μου Αβρααμ καὶ ὁ φόβος Ισαακ ...
= ... ho theos tou patros mou Abraam kai ho phobos Isaak ...
but also in a slightly variant form a few verses later, in v. 53:
ESV ... And Jacob swore by the Fear of his father Isaac
MT ... וַיִּשָּׁבַע יַעֲקֹב בְּפַחַד אָבִיו יִצְחָק
= ... wayiššābaʿ yaʿăqōb bĕpaḥad ʾābîw yiṣḥāq
LXX ... καὶ ὤμοσεν Ιακωβ κατὰ τοῦ φόβου τοῦ πατρὸς αὐτοῦ Ισαακ
= kai ōmosen Iakōb kata tou phobou tou patros autou Isaak
Rashi's discussion of the phrase suggests he thinks it is a (mere) epithet, and not a designation for Isaac's deity per se. This view seems to have prevailed up to the time of the seminal and influential studies of Albrecht Alt, in particular in his article, "The God of the Fathers".1
Since then, the phrase paḥad yiṣḥāq has been the subject of much debate, with a variety of suggestions about the precise meaning of paḥad itself ("thigh"? "kinsman"?), but these have been tested and found wanting,2 and the question that remains is that of OP: is this a reference to Isaac's deity ("Fear of..."), or to Isaac's experience of or posture before his deity ("fear of..")
It is a divine epithet: Alt made his case on the basis of (1) the "parallelism" with "God of Abraham" within the phrase of Gen 31:42, and the subsequent action in v. 53 (why would Jacob swear on his father's "emotion"?); and (2) the analogous phrase אֲבִיר יַעֲקֹב (ʾăbîr yaʿăqōb "Mighty One of Jacob") which is better attested and less contentious (Gen 49:24; Ps 132:2, 4; Isa 49:26; 60:16).
It's NOT a divine epithet: On the other hand, the phrase paḥad YHWH or equivalent is found numerous times in the Hebrew Bible, and so too of humans, as in e.g. Esther 9:3 (the "fear of Mordechai"). In these cases, however, the phrase conveys the fear produced by the figure(s) named, not the fear experienced by them. At a quick survey, paḥad seems consistently to be used of "terror induced by" rather than "terror experienced by".
Who knows? There appears to be no consensus on this. Still, two of the more substantial Genesis commentaries accept the "divine epithet" interpretation (Westermann and Wenham), although Westermann opts for understanding the phrase to mean "refuge" or "protection" of Isaac.3 (Wenham more explicit than Westermann, but in spite of this, the typography does not reflect the choice: both present it with lower-case: "fear", or "protection")
There are also two substantial and technical dictionary articles on the phrase.4 Both reject the "novel" suggestions for the meaning of paḥad and maintain the "traditional" understanding of "terror, fear". But Emile Puech (Anchor Bible Dictionary) upholds the "divine epithet" interpretation; Matthias Köckert (Dictionary of Deities and Demons) considers it "doubtful whether paḥad itself can be understood in terms of a divine name".
My own inclination is to go with the ESV for the following reasons:
- when paḥad is used in a phrase, it consistently means "fear induced by", and this sits uneasily in Gen 31:42 if it is not a divine epithet;
- the oath in Gen 31:53 would be odd if not sworn "on" a deity;
- the parallels noted by Alt are quite attractive;
- while there are considerations in favour of the "epithet" understanding, not much can be marshalled by way of argument/evidence against it.
Finally, the most recent full treatment of the phrase I'm aware of -- Lawrence Zalcman, "Shield of Abraham, Fear of Isaac, Dread of Esau", Zeitschrift für die Alttestamentliche Wissenschaft 117 (2005): 405–410 -- argues that the "divine epithet" understanding finds support in a new interpretation of the name of the Edomite god, "Qôs" = "dread" (see abstract at link).
- In translation in the collection Essays on Old Testament History and Religion (JSOT Press, 1989), especially pp. 26-27. Original publication date of the article was 1929.
- Against Albright's influential suggestion of "kinsman", see the thorough repudiation by Delbert Hillers, "Paḥad Yiṣḥāq", Journal of Biblical Literature 91 (1972): 90-92.
- C. Westermann, Genesis 12-36, (Continental Commentaries; Augsburg/SPCK, 1985) p. 497 (his chief grounds for the "refuge" interpretation is almost wholly based on Isa 2:10, 19, and the "fitness" of the epithet -- not a great argument, IMO); G. Wenham, Genesis 16-50 (Word; 1194), p. 278.
- E. Puech, "Fear of Isaac", in Anchor Bible Dictionary, gen. ed. David Noel Freedman (Doubleday, 1992), vol. 2, pp. 779-80; M. Köckert, "Fear of Isaac", in Dictionary of Deities and Demons in the Bible ed. by K. van der Toorn et al (2nd edn; Brill, 1999), pp. 329-31.