Toponyms are similar, but are named for a place rather than a person. For example, Lyme disease is a toponym, named for a town in Connecticut where the condition was first identified. In anatomy and medical circles, toponyms are often lumped together with eponyms. I'll do that here, too—because my explanations apply equally to both kinds of terms.
In Anatomy & Physiology, you may notice some things about the use of eponyms and toponyms that you are wondering about. So here's the scoop...
It turns out that this has been the trend for a quite a while, but only recently becoming widespread in use. For example, the American Medical Association (AMA) and other professional organizations that have something to say about terminology, recommend this approach. Because I think a textbook should reflect contemporary usage and engage with emerging approaches that have recently become mainstream, it makes sense to go in this direction.
Something else you may wonder about is that some eponyms are capitalized and others are not. For example, why are fallopian tube and eustachian tube not capitalized when Corti organ and Henle loop are capitalized?
Honestly, I only recently learned about this issue—when my copyeditor and I started going back and forth changing each other's terms from capitalized to lowercase, back to capitalized again, then lowercase again. It turns out that it's an increasingly common style to drop the capitalization when the person's name is converted to an altered form. As when Fallopius is altered to fallopian.
What is important to remember is that using possessive forms eponyms is not wrong. Nor is capitalizing Haversian canal. However, neither usage is in favor around many professional circles right now. My purpose is merely to explain why my usage may differ from the way you and I were trained.
You may also wonder why I usually relegate eponyms to only secondary or alternate status when naming structures and processes of the body. And you may wonder how we handle these changes in usage in a world where some professionals still use the older terminology. Those answers will have to wait until my next few articles. This one is already too long!