Tarentola gigas has been pushed back and forth between being a full species and being a subspecies of Tarentola delalandii. A recent molecular phylogenetic analysis showed the two species to be quite distinct (Carranza, S., E.N. Arnold, J.A. Mateo, and P. Geniez. 2002. Relationships and evolution of the North African geckos, Geckonia and Tarentola (Reptilia: Gekkonidae), based on mitochondrial and nuclear DNA sequences. Molecular Phylogenetics and Evolution 23: 244–256).
Specimens of Tarentola gigas gigas and T. g. brancoensis from Raso and Bronco islands were identical in terms of mitochondrial DNA (Jesus, J., A. Brehm, and D. J.Harris. 2002. Relationships of Tarentola (Reptilia: Gekkonidae) from the Cape Verde Islands estimated from DNA sequence data. Amphibia-Reptilia 23: 47-54). A single T. gigas from São Nicolau on the other hand showed rather large amount sequence divergence from the remaing T. gigas in the same study. I'm not sure anything further has been done with this.
Anyway, I'd say call them Tarentola gigas.
I hope this helps.
Tony