This is a good question. But it's kind of a conundrum, would we know about usurpers (usurpers since we know all of the legitimate emperors, and in any case a usurper is just an emperor that failed in his bid for power in a sense) if the damnatio memoriae was successful? How do we know about those we know of despite their very memoria seemingly being condemned to die and be lost to history forever?

In general there are three intertwined reasons why we do. First, and most importantly, the logistics involved in such a task were tremendous. A punishment of damnatio memoriae included both the destruction of the written name and visual and plastic representations of the person. That meant, in theory, every inscription, every portrait, medaillon, bust, statue, every coin stamped with the name and portrait of the emperor in question. Damnatio memoriae was one of the possible consequences of a sucessful condemnation for perduellio or crimen maiestatis, essentially high treason against the Roman people. Such a sentence only made sense for famous persons in the first place, those that had the means to commit such a crime and had public images and honorary monuments of themselves that mentioned their name, in the case of your question, the emperors. The publicly displayed image of the emperor was of such importance that we have portraits, inscriptions, coins and - sometimes crudely reworked from those of their predecessors - statues and busts even from those emperors who only ruled for a few months.

So if you are such a famous person, and in the times of the Empire, the damnatio memoriae was usually used against members of the imperial family and their friends and associates - most famously Geta, but also Caligula, Iulia Livilla, Messalina, Domitian and so on - there were a lot of things to manipulate. Statues and reliefs of the imperial family were ubiquitous, and inscriptions honouring them by name even more so - for example, (almost) every Roman milestone would start with the full name and title of the current ruling emperor, and often his sons as well. That's a lot of names to erase. Same is true for e.g. Papyri, where the name would have to be erased from every letter. That would have been easy with those still in the public archives, but less so for those officials had taken home with them. Then you had the countless coins, some of which were surely hidden away in some treasury or burial. So while in theory, every publicly written instance of the name was to be erased, the actual completion of such a task was all but impossible for a premodern empire with the level of bureaucracy the Romans had, especially considering the extent of the empire and the necessity to control the act over such a vast territory. There are lots of inscriptions surviving from Emperors and Princes who were supposed to have been punished by damnatio memoriae who survive in one area, but not in others.

The other problem is the logistics and the actual execution. We know of a lot of examples where the erasion of the Name of a person that was to be punished with damnatio memoriae was only superficially erased, as is the case in this inscription of Messalina - AE 1992, 739 -, where the name is still legible, though visibly damaged. The same is true in this inscription containing the half-heartedly erased name of Geta in line three - AE 1995, 1165. In many cases, the erasures are complete, or filled in again with new text, but examples such as those above show that such a practice did never completely remove the name (and in any case, since you had to remove material from the stone, the fact that something had been removed would have been obvious, and most people would have known what originally had stood there, especially if you could reconstruct it from other elements of the inscription. In fact, the highly formulaic nature of inscriptions, and especially the formal title of the Emperor, allows us today to reconstruct an Emperors name even without a name left simply from the titles and honours enumerated (well, ideally, reality of course is often more complicated). Say you have the usual formula honouring Septimius Severus and his two sons, there's the old man himself, followed by Caracalla and a big gaping hole in the stone - it's pretty clear that this was once the place where Geta's name was. Often, only the name is erased and not the titles, which makes reconstruction trivial for anyone interested in such details.

For what reasons such particular or clumsy erasions happened we can only guess. Maybe it was sympathy with the condemned, high workload, clumsy craftsmanship, analphabetism or simply carelessness, as in the case of a bronze table from Rome, where by mistake the name of Getas uncle (who had the same name) was erased, while Geta himself remained. It seems that the actual erasing was done most diligently in those provinces with a high military presence, where the imperial decree could hope for more people willing or being ordered to carry out the act, but not every province had a considerable military presence, and loyalists could easily throw a wrench or two into the whole operation.

Secondly, and most importantly, the practice of damnatio memoriae only considered public representation of the person in written name or in portrait. It didn't extend to the historical record or private comemmoration. This is why Livy can tell us, without a problem, about the case of M. Manlius Capitolinus, one of the earliest recorded cases (Liv. V.47, 1ff.), who had been condemned for trying to gain the kingship. And while Cassius Dio tells us that anyone even uttering or writing the name of Geta was immediately put to death (Cass. Dio LXXVIII.12, 5), he is proving himself a liar by writing about Geta using his name all the time, and Dio is writing in part during the reign of Caracalla. Historians could write about those who were punished by damnatio memoriae as much as they wished, and they did. The risk that an emperor could have been forgotten simply through damnatio memoriae is next to nil.

So then, why condemn someone to this ineffective and inconsistent practice in the first place, if it was impossible to execute to perfection anyway? That is the interesting question here, and the reason is that erasion from memory probably was never the goal. The goal was to manipulate remembrance of a person in a certain way. Charles Hedrick, in History and Silence (London 2000), p. 92-93, argues that 'political attacks on memory' were never an adequate measure to destroy the memory of a person; especially not with the tools available to a premodern state. Surely those persons who tore down the statue of Saddam Hussein during the fall of Baghdad or the statues of Lenin or Marx during the fall of the Soviet Union never for once imagined that they would be able to erase Marx, Hussein or Lenin from history. But the symbolic value of such an act is undeniable. Caracallas damnatio memoriae of Geta showed his victory over his brother and rival, his erasion from all the monuments that earlier had tried to show the strength and unity of the Severan dynasty, the concordia augustorum (the concord of the emperors), with the name of Geta replaced or erased showed that Caracalla was perfectly capable of stable rule alone (well we all know how that turned out, but that's propaganda for you). Geta is a bit of a special case in that Caracalla, with a very detailed set of implementary regulations disseminated into all corners of the Empire seemed to go further than most others before or after him, to have Getas name and image (unsucessfully, one might add) removed from every corner of the Empire. But Caracalla must have known that this would be unsuccesful, and that he could not have Geta removed from all the coinage as well (which, with its 'concordia Augustorum', unity of the emperors imagery and text, would have certainly given rise to cynical observations in those comparing them with the erased names and demolished statues of the new emperors brother). Florian Krüpe has interpreted this as an act of victors revenge, and an attempt to remove any doubt about the legitimacy and stability of his rule, to which the public presence of name and image of the brother he killed himself would have been a constant threat (F. Krüpe, Die Damnatio memoriae (Mörlenbach 2011), p. 252), and I think this is quite plausible.

So in a general sense, the target of such an act was never the memory of an individual per se, but the public image and the way a person was remembered in collective memory. There is a marked difference whether someone's name and image are kept alive, honoured by statues and inscriptions in the public space, or if he only appears as a traitor, a failure, a loser, in works of history or the spoken word. After the second world war, pictures of Hitler, that had before hung in almost every house, were taken down, same as statues of the dictator, and all over Germany and Austria, Adolf-Hitler squares, plazas, avenues and streets were renamed. That doesn't mean that he will be ever forgotten, but it marks a very tangible difference in how his name is kept alive in public memory. You won't find anything public named after Hitler in Germany, but that doesn't mean his damned memory isn't still alive.