How do we know so much about Roman Emperor Elagabalus?

I think you are misunderstanding the purpose of damnatio memoriae here. In general, the purpose of a Roman damnatio memoriae was not to erase all evidence that the person whose memory was being condemned ever existed, but rather to send a message that the person was no longer in power, that anyone who supported the person would be treated harshly under the new regime, and that the person was to be remembered negatively.

Steve Theodore, a friend I know from Quora who has an MA in ancient history from Brown University, wrote a well-informed and eloquent answer about damnatio memoriae a couple of weeks ago, in which he uses the infamous damnatio of Geta under Caracalla as an example. Here's an excerpt from the answer:

"The lack of subtlety here is precisely the point: Caracalla was not airbrushing Geta out of history like an old Bolshevik. Leaving the scars visible was a potent assertion of victory, an in-your-face reminder that Caracalla was in charge and anybody who didn’t like it was in trouble. The aftermath of the murder is said to have claimed 20,000 of Geta’s friends and supporters — Caracalla was not one for subtlety.""Roman damnatio was very effective in one critical way: it was visible and public. A crowd pulling down statues of Domitian, or the clink-clink-clink as a party of legionaries chiselled out the name of a deposed emperor was a very potent form of advertisment. In a world without mass media these displays were as electrifying as the televised toppling of a statue of Lenin or the dynamiting of the Bamiyan Buddhas."

[. . .]

"Damnatio memoriae was effective as a public dominance game: it was all about making it clear who was in charge, marking out the winners and losers in moments of intense conflict. What it was not, however, was a means of trying to censor the historical record — indeed, it brought about a kind of infamy which ensured it’s victims would long be talked about, albeit in hushed or scornful tones."

On top of this, even if the perpetrators of damnatio memoriae had wanted to erase all evidence that a person had ever existed, there's simply no way they could have effectively accomplished such a feat with respect to a person of such great fame and prominence as a Roman emperor who ruled for four years, reportedly attracted all kinds of scandal among the Senatorial elite, minted tons of coins with their name and face on them, and had tons of statues of themself set up all over the empire. Trying to erase such a person would be like trying to erase an entire U.S. presidency.

When it comes to Elagabalus (who was actually known to the public during their* reign as Antoninus and only received the nickname Elagabalus long after their death) specifically, there are plenty of coins minted during their reign with their name and image on them that have survived, as well as some portrait sculptures of them that managed to escape being defaced or recarved.

There are also three main surviving historical accounts of Antoninus's reign. Unfortunately, all these accounts were written by authors who vehemently despised them. The main contemporary sources for their reign are the accounts by Kassios Dion (lived c. 155 – c. 235 CE), a Greek historian from Bithynia who was a Roman Senator, and Herodianos (lived c. 170 – c. 240 CE), who was probably an equestrian from Syria.

Both historians wrote in Greek and both of them are deeply hostile to Elagabalus; they both portray the emperor as an effeminate and depraved tyrant. Herodianos, though, is somewhat less openly prejudiced toward them than Kassios Dion is, so his account is typically seen as a bit more trustworthy.

A third major source is the biography of Antoninus contained in the Historia Augusta, a notoriously untrustworthy collection of biographies of Roman emperors written in around the late fourth or early fifth century CE. The present scholarly consensus is that the biographies of the Historia Augusta are mostly fictional, but they can sometimes be used to supplement our understanding if treated with the appropriate caution and skepticism.

Like Kassios Dion and Herodianos, the Historia Augusta is deeply hostile toward Antoninus, but it also includes some truly bizarre and hilarious stories about their alleged antics. For instance, it claims that, upon assuming the consulship, instead of tossing coins to the masses as emperors usually did, they threw fatted cows, camels, donkeys, and slaves at them (Vita Elagabali 8.3) and that they liked to prank their guests by letting lions and leopards that had been trained not to hurt anyone into the dining room during dessert to give everyone a scare (Vita Elagabali 21.2).

One interesting thing is that, of the three main surviving accounts of Antoninus's reign, not a single one of them regularly refers to the emperor by their real name. Kassios Dion always refers to the emperor by names such as "Avitus" (which was the personal name they held before ascending to the throne) or "the false Antoninus" or "Sardanapallos," after the legendary Assyrian king whose alleged debaucheries are most famously chronicled by Diodoros of Sicily in his Library of History 2.23.1–2. Herodianos and the Historia Augusta both generally refer to Antoninus as "Elagabalus" after the Emesene sun-god Ilāh ha-Gabal whose worship they tried to elevate. This deliberate avoidance of the name that Antoninus was known by during their reign is arguably its own kind of damnatio memoriae.

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*I am using they/them pronouns for Antoninus on account of the historical ambiguity concerning their gender identity, which I discuss in this blog post I wrote two years ago. Kassios Dion in his Roman History 80.16.4 notably describes Antoninus on at least one occasion as insisting on being addressed as "κυρία," which means "lady" or "mistress," rather than "κύριε," which means "lord" or "master." Whether this account has any basis in historical reality is up for debate, but I figure that gender-neutral pronouns are the safest option to avoid misgendering.