According to the Merriam-Webster dictionary, an eponym is:
One for whom or which something is or is believed to be named.
A name (as of a drug or a disease) based on or derived from an eponym.
Eponyms are common in science.
Discoveries and innovations are often named after the discoverer or a figure who was influential in their advance (e.g., Avogadro constant, Alzheimer disease, and Apgar score).
In biological nomenclature, organisms often receive scientific names that honor a person. Examples include the plant Linnaea (named after Carl Linnaeus), the baobab Adansonia (Michel Adanson), and the moth Caligula (Roman emperor Caligula).
You might have noticed that I wrote "Alzheimer disease" and NOT "Alzheimer's disease." That is because English can use either genitive case (possessive) or attributive position (non-possessive) for the eponymous part of a term.
Grammarly will tell you that only Alzheimer's disease is correct, but the truth is that both "Alzheimer disease" and "Alzheimer's disease" are acceptable.
However, medical dictionaries have been favoring nonpossessive eponyms in recent decades. Additionally, the AMA Manual of Style recommends using nonpossessive forms.
Therefore, a medical writer or a medical translator will be more likely to use Alzheimer disease than Alzheimer's disease.
If you need medical writing or translation services, feel free to reach out!