Step 1: Graft Classifications.
- Autograft: Tissue transplanted within the same individual.
- Isograft: Tissue graft between genetically identical individuals (e.g., identical twins).
- Allograft: Tissue graft between genetically dissimilar individuals of the same species.
- Xenograft: Tissue graft between individuals of different species.
Step 2: Identification of Graft Type.
The term "genetically identical person" specifically denotes identical twins.
This scenario corresponds to an isograft.
Step 3: Final Answer.
Consequently, the appropriate designation is Isograft.