We don't know it for a fact, since Catullus never actually says so, but the attribution of the pseudonym to Clodia dates back to antiquity and is the only thing we have to go off of. Apuleius listed the true identities of four pseudonymic elegiac paramours in his Apologia. Propertius' Cynthia was apparently a woman named Hostia, Tibullus' Delia was Plania, and Catullus' Lesbia was Clodia (I forgot the fourth one). Apuleius was almost certainly using an earlier author's work as his source--Suetonius' fragmentary de poetis is often suspected. Whether that's right, god knows. The historical Clodia does, however, have a number of coincidental similarities to Lesbia. Her name, conveniently, scans the same as Clodia's, so it makes a great metrical substitute if that's who she really is. Lesbia is also rather...unsavory. Like Clodia she's known to have had several love affairs, often simultaneously--from Catullus we can identify no fewer than five lovers beside Catullus himself, plus her husband. She's also a rather nasty woman sometimes in Catullus, which would fit in with what Cicero says about her, though that's kind of a weak argument since Cicero is slandering a target that can't defend herself mercilessly, and in such situations he's prone to uttering complete nonsense for rhetorical effect. Famously, though, there's Catullus 79:

Lesbius est pulcher. quid ni? quem Lesbia malit/quam te cum tota gente, Catulle, tua./Sed tamen hic pulcher vendat cum gente Catullum,/si tria natorum suavia reppererit.

Lesbius is handsome. Why not [idiomatically that means something like "why shouldn't he be?" or "as he would be"]? Lesbia prefers him to you along with all your kind, Catullus. But still let this pretty boy sell Catullus with his kind, if he finds three kisses from his acquaintances [that is if he can find three people willing to vouch for him]

The phrase "Lesbius est pulcher" is often considered to be a camouflaged reference to Clodius' cognomem, Pulcher--that "pulcher" is used twice within such a short poem, when there are plenty of synonyms Catullus could use is certainly odd. Also odd is the description of Lesbius--Catullus speaks of him as though he were Lesbia's favorite lover, yet the fact that he just has Lesbia's name in the masculine suggests that they're related, surely siblings (and the position of their names at opposite ends of the line is striking). Of course, Cicero famously accused Clodius of incest with his sister, and it's traditionally thought that this is what Catullus is referring to. Also, Catullus' friend Rufus, with whom he had a falling out, described in Catullus 77 (though Catullus refuses to give details), is sometimes identified as Caelius Rufus, the subject of the Pro Caelio. Caelius was of an old and wealthy plebeian family, but until 55 or 54 when he was quaestor they were still only equestrian, only entering into the senatorial class with his quaestorship. Nevertheless he was active in politics as a prosecutor, and sometime around 57 had an affair with Clodia--Cicero's defense successfully argued that the prosecutor was being ordered by Clodia to use the crime of violence against an envoy as a means to get revenge for the end of their affair. Catullus also certainly knew Clodia--his family was a plebeian branch of the gens Valeria, one of the oldest families among the nobiles (although the Catullan branch hadn't done anything of note in a while--neither had Caesar's or Catiline's, so that doesn't mean that much), with both patrician and plebeian branches (note that the difference meant anything by this time--plebeian or patrician didn't mean anything, only nobilis or not did, that is whether your family had a consular ancestor or not. The Valerii of course did). According to Suetonius, Catullus' father entertained Caesar while he was in Cisalpine Gaul, where Catullus' hometown of Verona was, and Catullus was well-entrenched from his youth onwards in the upper-class strata. Catullus served in Bithynia under Memmius, who was married to a daughter of Sulla's and who probably served as his patron in some capacity--Memmius' wife, after their divorce, married Milo. Point is, Catullus surely knew Clodia and Clodius quite well, he was intimately acquainted with quite a lot of people who ran in the same circles as the two of them, and he himself ran in those same circles as well.

But there's no definitive proof, short of Catullus telling us. It's also possible that Apuleius means a Clodia totally unrelated to Pulcher's sister. But it's not an unreasonable guess