We have three names for ours - - oops, four (I can't count)
"the coop" (very subtle),
"The hen house" (again subtle),
"The chook house"
and "Peppi palace" (our top cluck at the moment is called Peppi)
I am not the most imaginative of souls...great names for everyone's coops - - egg plant
We have 2 main coops that have names. Original coop - Fort Duck. 2nd coop - Feather worth..WHAT? and now a few smaller ones no names on them just who ever is in them pen.