There is some debate about whether Paul is addressing a Jewish hypocrite or a gentile moralist in Rom. 2.1–16. I have historically held to the former option, though in my current reading of Romans I must admit that I'm seeing less and less that suggests a Jewish audience, either actually or rhetorically, encoded in Romans.
The situation seems to be clearer once we get to Rom. 2.17. In v. 17 Paul resumes the second-person singular address to an imaginary interlocutor, which he had first taken up in 2.1–6. The difficulties regarding Paul’s rhetorical audience in Romans 2 takes a significant turn in 2.17–20, where Paul offers an elaborate and extensive description of his interlocutor. First, Paul:
Εἰ δὲ σὺ Ἰουδαῖος ἐπονομάζῃ καὶ ἐπαναπαύῃ νόμῳ καὶ καυχᾶσαι ἐν θεῷ . . .
Ei de sy Ioudaios eponomazē kai epanapauē nomō kai kauchasai en theō . . .
But if you call yourself a Jew, and you find comfort in Torah, and you boast in God . . .
Paul says clearly that the rhetorical dialogue partner he to whom he pretends to be speaking calls himself [ἐπονομάζῃ; eponomazē] a Jew. According to Hans Bietenhard, eponomazō in Classical literature meant to “apply a word as a name, denominate, give a second name or surname, nickname.” When he turns to Rom. 2.17, Bietenhard rightly explains, “Here Jew is a title of honour, the heir to the legacy described in vv. 17–20. Paul attacks the inconsistency of claiming to be a Jew and at the same time countenancing sin.” However, in the very next sentence Bietenhard makes clear that he thinks the interlocutor in 2.17 does not simply claim to be a Jew but actually is one. Stanley Stowers agrees; Stowers imagines Paul, speaking as a Jewish missionary to interested gentiles, espying a fellow Jewish missionary in the audience and deciding to engage him in front of the letter’s gentile hearers. While the specific rhetorical strategy varies among commentators, most (if not all) agree that in 2.17 Paul imagines and addresses an actually Jewish interlocutor.
Given the weight of this consensus among commentators, I hesitate to offer my dissent. But I wonder if Paul might still be imagining a gentile moralist in 2.17, only now this gentile has taken on the yoke of Torah and, in contrast to the moralist of 2.1–6, worships the Creator God of Israel. If so, this gentile has taken on the name [eponomazē (2.17)] “Jew” and gone on to assume the signs of the Mosaic covenant, including circumcision (see 2.25–29). What is more, this gentile proselyte apparently has taken it upon himself to proselytize other gentiles within his sphere of influence (2.19–21). If this reading is right, the imagined interlocutor in 2.17–24 might be a Jew religiously but is a gentile ethnically. If so, then Paul has moved along a spectrum from morally depraved gentiles (1.18–32) through a morally elitist gentile (2.1–16) to a gentile who has not only assumed a more rigorous moral standard but has explicitly adopted a Torah-observant lifestyle.
As I said already, I offer this proposal cautiously and in full awareness that the breadth of insight and careful exegesis that belongs to Romans scholarship as a whole reads 2.17 at face value (i.e., that Paul addresses an ethnic Jewish interlocutor). Contrary to this impressive insight and exegesis, I suggest that the logical progression from 1.18–32 through 2.1–16 and on into 2.17–29 suggests that Paul tilts at a gentile proselyte who has assumed the name [eponomazō] “Jew.” The difference might not seem significant, but I think some interpretive problems arising from the rest of this paragraph (2.17–24) find some resolution if we take this exegetical option (I will flesh out this claim elsewhere).
But first, we need to take a moment to determine whether a gentile who commits himself to Torah-observance might “call himself a Jew.” Here the Stoic philosopher Epictetus provides a very interesting passage that may be relevant. As a Stoic philosopher, Epictetus is especially concerned that people claim the title philosopher without living out a philosophic way of life: “He is sharply critical of those who lightly call themselves philosophers but continue to ‘eat in the same fashion, drink in the same fashion, give way to anger and irritation’ (Discourses 3.15.10)—that is, to continue in a self-indulgent style of life totally at odds with the philosophical teaching they espouse.” In the context of critiquing those who call themselves one thing but live as another, Epictetus writes:
Why then do you call yourself a Stoic? Why do you deceive the many? Why do you act the part of a Jew, when you are a Greek? Do you not see how (why) each is called a Jew, or a Syrian or an Egyptian? And when we see a man inclining to two sides, we are accustomed to say, This man is not a Jew, but he acts as one. But when he has assumed the affects of one who has been imbued with Jewish doctrine and has adopted that sect, then he is in fact and he is named a Jew. Thus we too being falsely imbued (baptized), are in name Jews, but in fact we are something else. Our affects (feelings) are inconsistent with our words; we are far from practising what we say, and that of which we are proud, as if we knew it.
Admittedly, the key term, the verb eponomazō, does not appear here. When Epictetus speaks of “calling yourself” a Stoic, or people “being called” a Jew or a Syrian or an Egyptian he uses the more common verb λέγω [legō]. Later in this passage, when he refers to the genuine proselyte to Judaism, he uses the verb καλέω: “then he is in fact and he is named [καλεῖται; kaleitai] a Jew.” Though Epictetus does not prove that Paul has a gentile convert to Judaism in mind in Rom. 2.17 when he speaks of/to a person who “calls himself a Jew,” this text does raise the possibility that earning and exhibiting the epithet Jew was an issue for gentile converts to Judaism. “[T]he most significant aspect of the passage is that once they have taken this decisive second step and have fully adopted the Jewish frame of mind and way of life, the convert is seen, by Gentile outsiders at least, as fully a Jew, in fact as well as in name.”
 Hans Bietenhard, “ὄνομα” (part), NIDNTT 2.648. He carries this nuance forward into his discussion of eponomazō in the nt (see NIDNTT 2.655).
 Bietenhard, NIDNTT 2.655.
 “The Jews stand under the divine judgment like the Gentiles” (Bietenhard, NIDNTT 2.655).
 Stowers, Rereading, 142.
 Dunn, Romans, 1.109; Moo, Romans, 157–58; Schreiner, Romans, 127–30; Witherington, Romans, 85; Wright, “Romans,” 445–46. Jewett (Romans, 221–22) is ambiguous, but seems to agree.
 Pace BDAG (s.v.), which considers the compound verbal form equivalent with the simple ὀνομάζω (“ἐπι- without special mng.”).
 Terence L. Donaldson, Judaism and the Gentiles: Jewish Patterns of Universalism (to 135 ce) (Waco, Tex.: Baylor University Press, 2007), 389.