The only precise name is MDMA.

There's also "Molly," which is the street name for pure MDMA. (Though: most terms are tied to a specific geography.)

    ...nor would they know how to chemically identify if what they
    bought might contain MDMA.

True, but that's not unique to MDMA users. cf. the heroin in the Netherlands that was being sold as cocaine, and which lead to several deaths.

Organizations such as Dance Safe have existed for decades (in the U.S. at least) to let people test their drugs to make sure they're ingesting what they intend to ingest.