I have found a few definitions for a ‘syndrome’. I have come across medical definitions as well as psychological definitions. Here is a few…

A set of symptoms occurring together; the sum of any morbid state;
Any combination of signs and symptoms that are indicative of a particular disease or disorder.
The association of several clinically recognizable features.
A group of signs and symptoms that occur together and characterize a particular abnormality or condition.
A set of concurrent things as emotions or actions that usually form an identifiable pattern.

There are many syndromes…I ran across an abstinence syndrome…I even fund what is called organic brain syndrome

Down syndrome was given its name in order to recognize Dr. Langdon Down, who is credited in its discovery.