The diamond-shaped markings on the back are the kicker. "Bahamian" anoles is a pet shop trade name. Brown anole is the common name for A. sagrei. They are an introduced species, not native to the U.S. They originate in the Caribbean Islands area.
For anole care hints, I suggest you tune into the Anole Forum. There are many dedicated anole-keepers who are "Crazy About Anoles" on that forum and who will be happy to give you care hints for that adorable little baby.