Diseases are named after their discoverers, but there is not a possessive. Alzheimer disease was discovered by Alzheimer, not suffered by him. So it is not Alzheimer’s disease. Lou Gehrig had ALS, so it gets the possessive apostrophe: Lou Gehrig’s disease.
One common syndrome many people hear about is Down syndrome. Because syndrome starts with an s, many assume it is Down’s syndrome, but it is not; it just sounds that way.