OOOOh... while looking up hillbilly trivia, I discovered that the Clampett family from the Beverly Hillbillies were supposed to have moved to Beverly Hills from a town called "Bugtussle." Darned if that doesn't sum up a chicken's favorite pastime.
So if you dug the Clampetts, maybe "Bugtussle Chicken Eggs: fresh from the hills."
Think about the people that cannot recall your name when trying to locate you. I think you want something that leads them directly back to you. So if you sell eggs for the majority name should start with egg. So they find listings for egg whatever.
If chicks or chickens, same theory, chicken Annie or Chick A Dilly. Dumb suggestions but I am just saying when I forget a business, it is easy when the product is part of perferrable first word in the business name.