It seems on the one side Phoenicianist Lebanese politics supposes a common united and recognized identity of the Phoenicians and those scholars on the other hand, for example, Josephine Quinn, assert that they had virtually no common identity and thus cannot be considered a real people or civilization.
They seemed to have identified themselves according to their city, true, but so did the Greeks while having a general idea of Hellas. Can we say that these city-states had some sort of awareness of their common language, religion, and geography that united them, or is the idea of Phoenicia a fabrication?
The Phoenicians were Canaanites from the Lebanon. The Egyptians called them Sidonians because they traded with that city state the most. Phoenicians were still identifying themselves as Canaanite way up until the fourth (and possibly fifth) century in North Africa. Furthermore, we know that they still spoke Punic (a dialect of Phoenician) up until this time too (St. Augustine, The City of God). If Phoenicians in North Africa who have been conquered by the Romans and lost their hegemony still spoke Phoenician and referred to themselves as Canaanite over five hundred years since the destruction of Carthage, then it’s safe to assume that all Phoenicians had a common identity. This certainly applies to the Phoenicians in their original homeland in Lebanon. In addition, these very Phoenicians still worshipped the supremes Phoenician god and goddess Tanit and Baal, as evidenced by the archeological finds of graveyards and tombstones way up until the Roman era in North Africa.
When Hannibal was self exiled from Carthage, he fled to Tyre, Lebanon and lived there for several years. He likely had family ties there, as Carthage was founded by Tyrian colonialists. His escape rout to Tyre was one where he could make stops at areas where the Phoenician language was widely spoken, so that he could get around more easily (Reginald Bosworth Smith, Rome and Carthage: The Punic Wars). Furthermore, when Alexander the Great destroyed Tyre in 332 BC, many Tyrians fled to Carthage and spread their expertise there (Sanford Holst, Phoenician Secrets). As a matter of fact, Carthage boomed in prosperity, influence and power after 332 BC. Phoenician hegemony was no more in Lebanon and the Eastern Mediterranean, but their hegemony in the Western Mediterranean was as only getting stronger. This would later attract the prying eyes of the Greeks and Romans who wanted in on Carthaginian influence, trade and power.
Only full-blooded Phoenicians were given full Carthaginian citizenship. The local Berbers/Numidians could not become Carthaginian citizens. Those that were of mixed Phoenician and Berber heritage (50-50) were able to attain some citizenship rights, but not all the rights enjoyed by the Phoenicians in Carthage (Adrian Goldsworthy, The Punic Wars).
Sources:
St. Augustine, The City of God
Reginald Bosworth Smith, Rome and Carthage: The Punic Wars
Sanford Holst, Phoenician Secrets
Adrian Goldsworthy, The Punic Wars
See also:
Hannibal - Exile and Death (Encyclopedia Brittanica)
Phoenicia.org, an excellent resource on the Phoenicians.