Ordinary people call it alphabetic. Scholars also follow suit.
Alphabetic.
Code
hieroglyphics
A person who studies writing can be called a linguist or a philologist, depending on the specific focus of their study. They may also be referred to as a literary scholar or a composition specialist.
Archaeologists call the basic unit in the Aztec and Mayan system of writing is called a glyph.
pedagogue
You call that person a scholar.
Archaeologists call the Sumerian writing system "cuneiform". We do not know what the Sumerians called it.
A biologist.
I guess an eager scholar?
Counter-evidence that could call Shaffer's thesis into question would include historical records or archaeological findings that support a different origin story for the alphabet, such as a single inventor or a different geographical region where writing systems originated. Additionally, evidence of earlier or contemporary writing systems that predate the Phoenician alphabet could challenge Shaffer's claim of its innovative and influential nature. Moreover, linguistic or comparative studies showing significant differences or lack of connection between the Phoenician alphabet and other writing systems might also cast doubt on Shaffer's thesis.
Punicus was their word for Phoenicians - Carthage was originally a Phoenician colony.