1. An eponym is a place or thing which takes its name from a person (living or dead, real or imaginary). In the language of medicine, eponyms abound. Surgical instruments, medical devices, operative procedures, and anatomic structures are frequently named after the person who made the discovery or invention. An eponym that is used as an adjective is usually capitalized; the noun which follows is not.
Lyme disease Down syndrome
Tinel's sign Kirschner rod
Buck's fascia Achilles heel
2. A word derived from an eponym is generally not capitalized.
cesarean section (from Julius Caesar)
parkinsonian (from Parkinson's disease)
kocherized (from Kocher clamp)
jacksonian seizure (from Jackson)