What do you call the little things stuck in the corners of your eyes after you wake up in the morning?

Mattering. This is just dried secretions from the eyes that flow to the outside, become dried and crusted and you can visibly see it. A warm face cloth or a shower or gentle rubbing will get rid of them. If there is pain, redness, swelling or other concerns, you may need to see a health care professional. Some call them "eye boogers".
Dried discharge. May be made up of pus (dried up white blood cells and debris due to conjunctivitis ) or just residual mucous from dried tears that evaporate after seeping onto the skin while sleeping.