The phrase "breed designation" refers to a label or classification given to a specific animal based on its distinct characteristics or genetic lineage. It helps identify the breed of the animal. Full definition
They must be given a primary breed designation, even if such a designation does not match reality. (stopbsl.org)
Terriers all resemble each other and indeed may have common ancestry, but breed designation in this group may or may not be proof of separate development. (canismajor.com)
just to satisfy their curiosity, dog breed designations have also been used in an attempt to predict future behavior, match pets to families, find lost dogs, and even to restrict the ownership of certain types of dogs. (sheltermedicine.vetmed.ufl.edu)