Single Word for Hair Clog
Solution 1:
A more general term for a sewer blockage is a fatberg about which Wikipedia says
a congealed mass in a sewer system formed by the combination of non-biodegradable solid matter, such as wet wipes, and congealed grease or cooking fat.
Fatberg is a neologism from a combination of the words fat and berg, modelled on iceberg.
The Cambridge Dictionary has
fatberg
noun
UKa large mass of fat and waste material that forms in sewers (= waste pipes under the ground)
and also in Collins, and others.
Solution 2:
Drano.com uses the term hair clog.
But, they also say:
... here are 5 great ways to prevent hairballs from being your downfall.
Drano, for those who aren't familiar with it, is a product designed to unclog drains by dissolving the oils, fats, and other accumulations that cause clogs.
I'd say that if you need a single word, use hairballs. It's recommended by the experts.
Interesting side note, if the clog were in the intestines rather than a pipe, it's called a bezoar. When made of hair, specifically it's a trichobezoar.