Carthage was a colony of the Phonecian cities Sidon and Tyre, also called the Caananites in Scripture. The Caananites had a god called Moloch to who children were sacrificed. This practiced also migrated into Israel and Judah where it is routinely condemned in Scripture.Yes, the Romans referred to the Carthaginian people as Punic, presumably a derivation of Phoenician. I also have read that the Carthaginians would have worshiped Baal, and that names like Hannibal means something like "Baal helps him". So, they, or their forbears are alluded to in the Bible, but the Carthaginians proper, who fought the long war(s) with Rome are not, AFAIK.
Hanibal means "Graced by Ba'al".
Not all cities in the Phonecian Empire are directly mentioned. But their culture and religion are. After Persia conquered Sidon and Tyre, Carthage took over and expanded the empire.