Neither Greek nor Latin really do honorifics of the same sort as English. There is no "Mister" or "Madam" in Greek. The use of the vocative case of an individual's name--technically grammatically required in all direct speech, but identical in form to the nominative in many nouns (and there are ways to get around it)--would generally have been polite enough. Greeks moreover did not have surnames, but they did have patronymics that were often used as polite terms of address. So in Homer Zeus is frequently called Kρονίδη, the vocative of Κρονίδης, itself the patronymic of Κρόνος, even by his own children. In most forms of Classical Greek the "epic" patronymic in -ίδης had dropped out as a true patronymic form, and instead was mostly used in personal names (e.g. Λεωνίδης, Doric Λεωνίδας, whose name literally means "lion's son") with no true patronymic meaning. In Attic as in other dialects in the Classical Period the patronymic simply took the form of the father's name in the genitive. Hence Πηληiάδεω Ἀχιλῆος, "Achilles son of Peleus," in Homer but Ξενοφῶν ὁ τοῦ Γρύλλου, "Xenophon son of Gryllus." Or more simply (but in rather lacking style) Ξενοφῶν ὁ Γρύλλου or Ξενοφῶν τοῦ Γρύλλου or even simply Ξενοφῶν Γρύλλου (the worst of the lot, really). Other members of an individual's family might be appended to this, sometimes really getting out of hand. So Plato has the character of Socrates refer to Ἱπποκράτης ὁ Ἀπολλοδώρου ὑὸς Φάσωνος δὲ ἀδελφός, "Hippocrates son of Apollodorus and brother of Phason." In the case of women the father was often (though not always) replaced with the mother or a woman's patronymic was replaced entirely or supplemented with her husband's name in the genitive. Just to take the first example quoted from Schaps' The Woman Least Mentioned: Etiquette and Women's Names:

οὗτος ἔλαβε Ξεναινέτου Ἀχαρνέως θυγατέρα, ἐξ ἧς γίγνεται Κυρωνίδης καὶ Δημοχάρης καὶ ἡ μήτηρ ἡ ἐμὴ καὶ ἄλλη τούτων ἀδελφή

He married the daughter of Xenaenetus the Acharnian, and from her were born Kyronides and Demochares and my own mother, another of their sisters.

This habit of only providing a woman's patronymic, in whatever form, and never supplying her personal name at all is par for the course. Note also the presence of a demonym, Ἀχαρνέως "of Acharnae." In Athens and other cities divided into demes (e.g. Eretria) one's deme was indicated by the genitive of the deme. Hence Alcibiades is identified as Αλκιβιαδης Κλεινιου Σκαμβωνιδης, "Alcibiades son of Clinias of the deme of Scambonidae," in an ostrakon supporting his ostracism. Note that Σκαμβωνιδης is in form identical to the Homeric patronymic in -ίδης. Demonyms might have other forms, such as Xenaenetus' above: the singular nominative of his demonym would be Ἀχαρνεύς, from the deme of Ἀχαρναί. An alternate form Ἀχαρνηίδαι (pl.) is also recorded. Laconia of course had no demes, but just as an Athenian in a foreign city referred to himself and was referred to as an Athenian so would a Spartiate in a foreign city. So Xenophon introduces himself in the Anabasis with: ἦν δέ τις ἐν τῇ στρατιᾷ Ξενοφῶν Ἀθηναῖος, "there was a man in the army, Xenophon, an Athenian." Or, from the Protagoras, Ἱππίαν τὸν Ἠλεῖον (nominative Ἱππίας ὁ Ἠλεῖος), "Hippias the Elian" (more usually translated as Hippias of Elis).

In Athens of course women seldom entered into the public sphere of men, and although the status of women in Laconia was hardly so equal as some on the Internet would pretend to believe a Spartiate woman had a somewhat better chance of being spoken to directly in public. There is, however, not very much textual evidence whatsoever for Laconian speech. Interestingly in the Lysistrata none of the women--Athenian, Boeotian, or Spartan--ever refer to each other by patronymics or anything like that, which might suggest that the use of patronymics for women is mainly employed when speaking of them in the third person or on the inscriptions (usually funerary) on which we find their names. But then again the only time a patronymic is used in the play is a brief reference to the sons of Tyndareus, i.e. Castor and Pollux. Famous women, Spartan or not, of the sort whose names were considered worth including in pieces of literature, might well receive a rather full treatment. For example, Herodotus introduces Gorgo as τῷ Κλεομένεϊ ἡ θυγάτηρ, τῇ οὔνομα ἦν Γοργώ, "the daughter of Cleomenes, whose name was Gorgo." But Herodotus does that regularly with people who actually get names, and Gorgo grew up to be a queen.

In Greek, as I've said, the vocative is usually enough. But one's name did not have to be used at all. Vocative forms exist for, at least theoretically, all nouns, and Greek is further blessed with the so-called "vocative noise," ὦ. When not used as an exclamatory (oh!) ὦ is simply placed in front of a vocative noun (often written ὤ in such cases) as a part of the direct address--note also that the Greek imperative can also take ὦ, it being an item of direct address itself. Hence ὤ Σωκράτη, which is more or less equivalent simply to Σωκράτη, the vocative form of Σωκράτης. In Attic frequently the vocative noise was added to nouns other than names as a sort of specially polite mode of direct address. So again in the Protagoras Socrates calls an irate doorman ὠγαθέ, the vocative of what would be ὠγαθός, except that that word doesn't exist because this particular form is a contraction of ὠ ἀγαθέ, the vocative of ἀγαθός, "good." Thus it only exists in the contracted form in the vocative since the vocative noise only appears in front of a vocative. This is the masculine singular form: theoretically (though no examples come to mind, and I do not believe it to be attested) one might use the feminine vocative ἁγαθή and construct ὠγαθή from it. That's Attic, however. In Doric the feminine vocative singular of the same adjective is ἀγαθά. Attic--the only dialect for which we have much evidence for colloquial speech whatsoever--had many of these sorts of things. So in the Apology Socrates addresses the Assembly, as was more or less normal, as ὦ ἄνδρες Ἀθηναῖοι: "men of Athens" but really something more resembling "gentlemen," colloquially. In theory one might say ὦ γύναι, "woman" (Attic sing. nom. γυνή, Doric γυνά. I believe the Doric vocative was identical to the Attic in this noun, but I'd have to look it up). Men in Attica at least frequently referred to women simply in this way, just with the vocative of γυνή. Note that Socrates uses ἀνήρ rather than ἄνθρωπος. Both mean "man," although ἄνθρωπος really means "person," Latin homo--ἀνήρ is cognate with Latin vir, and really refers specifically to a male as opposed to a woman, rather than a human as opposed to an animal. The corresponding phrase ὦ ἄνθρωπε (or more usually contracted, ὦνθρωπε) is attested, but rather than a term of polite speech it's usually (though not at all always) insulting and applied to slaves or people you want to insult. Dickey in The Ancient Greek Address System and Some Proposed Sociolinguistic Universals points out that by the Roman Period κύριε, the vocative of κύριος (literally "master," but more like "lord") appears sometimes as a sort of pseudo-honorific in the style of Mr/Mrs--note however, that it usually stands by itself and is rarely affixed in front of something (e.g. κύριε μου πάτερ, "my lord father"--I can think of no example off the top of my head where it's in front of a name). This is thoroughly anachronistic for any period in which we might realistically refer to "Spartans," even considering their period as an irrelevant political power after the early fourth century or so. There's a further problem here in the general lack of a Laconian written record, much less a colloquial record. Spartan society was heavily stratified, with Spartiates (similars and inferiors), perioeci, allies, tributaries, helots, slaves, etc. all existing within the same space. Presumably a helot might, as Athenian slave did to their masters, speak to a Spartiate as ὦ δέσποτα (nom. masc. δεσπότης, fem. nom./voc. δέσποινα. I believe the Doric vocatives are identical to Attic), but did a perioecus? Would a perioecus use the vocative form of Σπαρτιάτης, which should be Σπαρτιᾶτα (fem. voc. Σπαρτιᾶτις--Doric nom. masc. Σπαρτιάτας, however, and whatever the hell the feminine would be) which is rarely, if ever, attested? Moreover, what the hell do we mean by "upper-class" here? Strictly speaking Spartan law did not recognize the existence of such a concept, though in reality the Similars were hardly similar at all, and the Inferiors were by their very nature socially and economically lesser, though still in Laconian society as a whole the social elite and leisure class. Unless we mean perioeci or helots speaking to full Spartiates it's hard to define the meaning of the term "upper-class," and harder still to conceive of what manner an "inferior" Spartiate (capital I or not) might speak to, say, the wife of an ephor in a society that pretended to practice strict equivalence between all members of the leisure class.