The verbal adjective κλειτός is used in a wide range of Greek epithets/proper names. It appears in compounds such as Πολύκλειτος (much-famed), δουρίκλειτος (spear-famed), τηλέκλειτος (far-famed) and περίκλειτος (famed all round).
In light of these examples, what would the Greek name Παράκλειτος actually mean? We can see it attested in this website for example, which mentions a person named Παράκλειτος Στεργίου.
I am not an expert, but I fear this is not how I'd spell that last name. Now, η and ει were mightily confused in 2nd Century Egypt and Testament Koine, because of their similar sounds; and were the source of one of the commonest spelling mistakes then, in my impression [Simos Menardos' Oxford Lectures]. They quickly devolved to a long e, and a long i, respectively, and merged into the latter.
The common Christian name is actually Παράκλητος, from καλέω to call, summon, (LSJ)
- called to one's aid, in a court of justice : as Subst., legal assistant, advocate, D.19.1, Lycurg. Fr.102, etc. 2. summoned, “δοῦλοι” D.C.46.20, cf. BGU601.12 (ii A.D.). II. intercessor, Ph.2.520 : hence in NT, Παράκλητος, of the Holy Spirit, Ev.Jo.14.16, cf. 1 Ep.Jo.2.1.
so, with παρά, by its side, emissary/flunky of the Holy Spirit. (Several religious sites translate it as "comforter", somebody you, or the Holy Spirit, call by you to help you out in distress?)
This is in contrast to the verb κλέω, κλείω,
tell of, make famous, celebrate, “ἔργ᾽ ἀνδρῶν . . τά τε κλείουσιν ἀοιδοί” Od.1.338, cf.h.Hom.32.19; “ἐγὼ δέ κέ σε κλείω” Od.17.418, cf. Hes.Op.1, Th.105, Stesich.35, Inscr.Cos 218.7, prob. in Hermesian.7.33; “ἔν τ᾽ ἀλύροις κλέοντες ὕμνοις” E.Alc. 447; “Θέτιν . . κλέουσαι” Id.IA1046; κλέωἁ τὸν Ἀμύκλαις σιόν, Lacon. for κλέουσα τὸν Ἀμ. θεόν, Ar.Lys.1299:—Med., “γῆρυν, ἃν σοφοὶ κλέονται” E.Fr.369.7:—Pass., to be famed: c. dat., for a thing, φρένες . . ᾗς τὸ πάρος περ ἔκλε' (for ἐκλέεο) Il.24.202; “ἐγὼ δ᾽ ἐν πᾶσι θεοῖσι μήτι τε κλέομαι καὶ κέρδεσιν” Od.13.299; κλέεσθαι ἐν φορμίγγεσσι to be celebrated in lyric strains, Pi.I.5(4).27; ἔνθ᾽ . . ἀγοραὶ Πυλάτιδες κλέονται where are held the famous meetings, prob. in S.Tr.639 (lyr.). II. c. acc. et inf., sing how . . , B.15.13. (κλεϝ-, cf. κλέος, κλὐω, Lat. clueo: Skt. śrutás ( = κλυτός) 'famous', śṛṇóti 'hear'.)
which has led to all other glory/renoun names you mentioned above,
κλειτός , A.renowned, famous, “ἐπίκουροι” Il.3.451, 6.227, etc.; “βασιλῆες” Od.6.54; “γενεά” Pi.N.6.61; of things, splendid, excellent, “ἑκατόμβη” Il.4.102, cf. Pi.P.10.33; Πανοπεύς, Ἰωλκός, Il.17.307, Pi.P.4.77.
my favorite being Ἡράκλειτος.
