Hello there! As /u/Smackaroo already pointed out here, Hannibal's Phoenician name was probably ḥnb‘l (transliterated here into the Latin alphabet; the Phoenician alphabet has no vowels)--a very common Phoenician-Punic name. His family name is more problematic, however, as surnames and cognomina are almost never attested in Phoenician-Punic texts beyond the occasional gentilic. Various commentators have suggested brq meaning "lightning," but a more plausible candidate (in my view, at least) is brk meaning "blessed," which appears much more often in the ancient inscriptions. Thus, his whole name might look something like ḥnb‘l hbrk (h being the definite article). Yet assuming that Hannibal followed the cultural norms of his homeland, he would more likely identify himself simply as ḥnb‘l bn ‘bdmlqrt (bn ḥnb‘l), or "Hannibal son of Abdmelqart [=Hamilcar] (son of Hannibal)," listing his father and perhaps grandfather. I hope you find this helpful! :D