What does it mean that 35% of named persons in Romans 16 are women?

The number is not the point on its own. A high-female-share list could in principle be a list of background figures named for politeness. What makes Romans 16 different is that the role-vocabulary attached to the women is the same role-vocabulary Paul uses of himself and of his named co-workers everywhere else.

A direct count of Romans 16:1-15 yields approximately 26 named persons. About 9 are women — Phoebe (v. 1), Prisca (v. 3), Mary (v. 6), Junia (v. 7), Tryphaena and Tryphosa (v. 12a), Persis (v. 12b), Julia (v. 15), and Nereus's sister (v. 15). Rufus's mother (v. 13) is named-by-relation. About 17 are men. The female share is roughly 35 percent — the highest in any large Pauline greeting list.

For comparison, three other late Pauline greeting passages:

The Romans share is not just numerically the highest. It is the largest absolute number of named women in any single Pauline passage by a wide margin.

What matters more than the count is the role-vocabulary. Six of the nine named women in Romans 16 receive a Greek role-word from a closed lexical set Paul uses elsewhere in his letters of himself, of his named co-workers, and of the local leaders churches are commanded to honor:

Five separate role-words: diakonos (G1249), prostatis (G4368), synergos (G4904), kopiaō (G2872), and episēmos + apostolos (G1978 + G652). Each one of them is attached, elsewhere in Paul's letters, to recognised co-workers — the named men of his missionary circle and the named officers of his churches.

Diakonos (G1249) at Rom 16:1 is the same lemma in the same accusative case-form as διάκονον in Rom 15:8 — applied to Christ Jesus, in the same letter, one chapter earlier. Across the New Testament the lemma is applied to Christ, Paul, Apollos, Timothy, Tychicus, Epaphras, and the formal office-holders at Philippi (Php 1:1) and Ephesus (1 Ti 3:8, 12).

Prostatis (G4368) is a New Testament hapax with 0 LXX occurrences. The cognate verb προΐστημι (G4291) is Paul's standard leadership-verb: Rom 12:8 (ὁ προϊστάμενος); 1 Th 5:12 (τοὺς προϊσταμένους ὑμῶν ἐν κυρίῳ); 1 Ti 3:4-5, 12 (deacons "managing" their houses); 1 Ti 5:17 (οἱ καλῶς προεστῶτες πρεσβύτεροι — "elders ruling well"). The 8 LXX occurrences of the verb (2 Sam 13:17; Amos 6:10; Isa 43:24; Ezk 48:35; Pro 23:5; 1 Mac 5:19; 4 Mac 11:27, plus a doublet) are all leadership or oversight. There is no "helper" sense in the LXX.

Synergos (G4904) is applied across the Pauline corpus to Timothy, Apollos (1 Cor 3:9 — Paul + Apollos θεοῦ συνεργοί), Titus, Epaphroditus, Clement, Mark, Aristarchus, Demas, and Luke. Prisca is in that list. Philippians 4:3 confirms the praxis from a second letter: Euodia and Syntyche συνήθλησάν μοι ἐν τῷ εὐαγγελίῳ (G4866) and are counted among τῶν λοιπῶν συνεργῶν μου — the same word.

Kopiaō (G2872, "to toil to exhaustion") attaches to four named women in Romans 16 (Mary, Tryphaena, Tryphosa, Persis). Persis's ἐκοπίασεν (V-AAI-3S) is the same tense, voice, and mood as Paul's ἐκοπίασα (V-AAI-1S, 1 Cor 15:10), differing only in grammatical person. The titular τὰς κοπιώσας ἐν κυρίῳ of Tryphaena and Tryphosa is morphologically the same shape as 1 Thess 5:12 τοὺς κοπιῶντας ἐν ὑμῖν — the recognised Thessalonian leaders the church is commanded to honour. 1 Tim 5:17 says elders of "double honour" are μάλιστα οἱ κοπιῶντες ἐν λόγῳ καὶ διδασκαλίᾳ. 1 Cor 16:16 commands the church to ὑποτάσσησθε "everyone working alongside and labouring." The lemma does not segregate Paul's kopiaō from the women's.

Episēmoi en tois apostolois at Rom 16:7 — the contested phrase about Junia — sits inside an empirical embedding field that is uniformly composed of prominence/conspicuousness/renown words, and inside an LXX usage pattern (9 of 9 occurrences) that is uniformly internal designation. The category apostolos (G652) in NT usage is broader than the Twelve, including Barnabas (Acts 14:14), James (Gal 1:19), Apollos (1 Cor 4:9), and Epaphroditus (Php 2:25).

The cumulative observation is that a closed lexical set of role-words attaches to six of nine named women in Romans 16, and the same closed set attaches elsewhere in Paul's letters to himself, to his named male co-workers, and to the local leaders churches are commanded to honour. This is descriptive data. It is what Romans 16 says.

What it does not say is the synthesis question. It does not by itself tell us how this praxis-vocabulary relates to the prescriptive instructions of 1 Corinthians 11/14 and 1 Timothy 2. The same letter that contains the doctrinal argument of Romans 1-15 contains the greeting list of Romans 16. Both belong to Paul. The work of integrating the two — sorting which prescriptive instructions are creation-order, which are covenant-specific, and which are first-century social-convention engagements — belongs to Part 9 of the series.

What this answer can settle is the descriptive datum. Nine named women. Six role-words from a closed lexical set Paul uses of his recognised co-workers. The female share is the highest of any large Pauline greeting list. The role-words are the same role-words. The text reports both, in the apostle's own Greek.

For the full Romans 16 analysis — the role-word table, the cross-letter Pauline distribution, and the Sirach contrast for cultural backdrop — see Phoebe, Priscilla, Junia: What the Greek Calls the Women.

For the prescriptive-side passages this descriptive data sits alongside, see I Do Not Permit a Woman to Teach: Three Commands, Three Problems and Wives Submit, Husbands Love: The Household Codes.