The medical term for "eye boogers" is "rheum." I found it!

nasal discharge
may be unilateral or bilateral, serous, purulent, hemorrhagic, or contain food material. http://medical-dictionary.thefreedictionary.com/nasal+discharge

Rheum is a medical term for the natural mucus discharge from the eyes, commonly known as matter, sleepydust, sleepers, sleepies, sleepy men, sleepy seeds, eye boogers, eye gunk, eye goopy, gound, or legaña. The discharge forms a crust on the eyelids, or gathers in the corner of the eye during sleep (contrast to mucopurulent discharge). It is formed by a combination of mucus consisting of mucin discharged from the cornea or conjunctiva, tears, blood cells, skin cells from the eyelids, and dust.
Normally, blinking causes this substance to be washed away with tears. The absence of this function during sleep, however, results in a small amount of dry rheum forming in the corners of the eyes even among healthy individuals, especially children. Still, the formation of a large amount of crust or the presence of pus within it may indicate dry eye or other more serious eye infections including conjunctivitis and corneitis.
Adults and older children can easily remove the crust by washing the eye with water or simply brushing it away with clean fingers. In young children, however, the buildup of rheum can be so severe, that opening one's eye upon awakening can be difficult or impossible without washing the eye. Very young children or people under care may need to have this done by another individual.
http://en.wikipedia.org/wiki/Rheum

Why do we wake up with “crusties” or “sleep” in our eyes? — Aaron Craig, Cordova, TN
Dear Craig:
People have given that “stuff” we get out of our eyes in the morning many different names. Some call it “matter”; others call it “sleep,” “sleepy,” “crusties,” or “eye boogers.” But whatever it is called, there is no denying that we all have it and would like to know what it is.
Many years ago, some scientists said that evolution was a fact because the human body supposedly contained parts that didn't do anything. For a long time it was thought that organs such as the tonsils and the appendix were useless “leftovers” of evolution. These parts were called vestigial (ve-STIJ-ee-al) organs. The word “vestigial” means a trace or a mark left by something, much like a footprint. It was thought that these “useless” organs were marks or “footprints” of evolution.
One of those organs was the plica (PLY-ka) semilunaris (sem-ee-LOO-ner-is), which is located around the eye. For many years, this organ was thought to have no function. But lo and behold, eventually it was discovered that this “useless” organ has an important function after all.
In fact, it is the “crusty” factory. It secretes a sticky mass that collects any foreign materials such as dust or pollen. All this trash is surrounded by the sticky gook so that it does not scratch the sensitive cornea in your eye. Once the garbage is collected, the plica semilunaris “escorts” it out of the eye just like a security guard would escort noisy troublemakers out of a theater.
Let’s all give the plica semilunaris a big hand for doing such a great job of “taking out the trash” in our eyes. And remember, there are no “footprints” of evolution in your body because your body did not evolve-God designed it!
http://www.discoverymagazine.com/digger/d01dd/d0101dd.html