Bechet's disease- Turkish dermatologist ophthalmostomatogenital syndrome

Bechterev disease ankylosing spondyloarthritis

Fuks syndrome - uveitis

Wilson disease

Parkinson disease

Alzheimer disease

Dear Marianne Levon Shahsuvaryan, thanks for your answer. When I reach a certain answer / number, I will collect all the names of diseases as a list.

Irvin-Gaas syndrome - macular edema after cataract extraction

Shtardart disease conjenital macular degeneration

Coats disease

Morax-Axenfeld angular conjunctivitis

Mooren corneal ulcer

Dear Marianne Levon Shahsuvaryan and Joy Mutheu, thanks for your answers. I hope the list will be comprehensive after the contribution of such valuable answers.

Schegren disease

In my question I gave the names of four diseases as example. In the following days 33 new names mentioned in the valuable answers. Most of the new stated names are the syndrome names. I expect increasing the number with the new answers. Then I will collect all the names in a detailed list of diseases and syndromes and share them on this platform.

You are searching for eponymously named diseases. You may need to separate out the ones named for famous poersons with the disease from the ones named after their discoverers, but here's a _much_ longer list than you have so far:

https://en.wikipedia.org/wiki/List_of_eponymously_named_diseases

Dear David Winsemius, thank you very much for your valuable contribution.

Botkin's disease - Hepatitis

Bekhterev disease - ankylosing spondyloarthritis

Mikulich disease

Terson's syndrome - subarachnoid and retinal hemorrhage

Dear Marianne Levon Shahsuvaryan, thanks for your contribution to this subject from the beginning of the question.

In 1984, research groups led by Dr. Gallo, Dr. Luc Montagnier at the Pasteur Institute in Paris, and Dr. Jay Levy at the University of California, San Francisco, all identified a retrovirus as the cause of AIDS. Each group called the virus by a different name: HTLV-III, LAV, and ARV, respectively.