Formal:
* Reptile Sanctuary
* Reptile Center
* Herpetological Institute
* Reptile Conservation Facility
Informal:
* The Reptile House
* Scales and Tails
* The Lizard Lounge
* Slithering Haven
* Cold-Blooded Critters
* The Reptile Retreat
Creative:
* The Serpentarium
* The Dragon's Lair
* The Turtle Temple
* The Gecko Grotto
* The Iguana Oasis
The best name will depend on the specific reptiles you house, the overall theme of the facility, and your personal preference.