Why is the Pope's Twitter handle @Pontifex?
It's taken from one of his official titles, which is Supreme Pontiff of the whole Church, pontifex being the Latin word that we translate into English as pontiff. Supreme Pontiff in Latin is Summus Pontifex.
Pontifex dates back to long before Christianity, quite likely as far back as Rome's second king, Numa Pompilius (715–673 BC). It meant a member of the College of Pontiffs, the body overseeing Rome's religious practices. The director of the College of Pontiffs was the Pontifex Maximus.
Dionysius of Halicarnassus (c. 60 BC – c. 8 BC), a Greek historian, offered the first etymological explanation that we know of for the term pontifex, writing that it means "bridge-builder" (the Latin words pons and facere), but other interpretations were also offered.
During the reign of Rome's second emperor, Augustus, which started in 27 BC, the office of pontifex maximus became one of the emperor's. It remained an office claimed by all emperors until Theodosius I, Roman emperor from AD 379 to 395. With Theodosius I's Edict of Thessalonica in 380, Christianity became the official religion of the Roman Empire, having been formally legalized—along with all religions in the empire—by the Edict of Milan in AD 313 under Emperor Constantine. Eventually under Theodosius, other religions were banned.
Pope Leo I, whose papacy was from 440 to 461, was the first pope to adopt the title Pontifex Maximus though the bishop of Rome had been referred to as pontifex maximus in a more general sense in writings as far back at the 200s.
During the Italian Renaissance, which started in the 1300s, when the history and culture of ancient Rome was being rediscovered and capturing the imaginations of artists, scholars, and patrons, various popes styled themselves Pontifex Maximus, including in inscriptions on public works they funded, such as fountains, many of which can be seen in Rome today.
But the Pope's official titles don't include Pontifex Maximus. Or Pope, either!
In English, Pope Francis' titles are:
Bishop of Rome, Vicar of Jesus Christ, Successor of the Prince of the Apostles, Supreme Pontiff of the Universal Church, Primate of Italy, Archbishop and Metropolitan of the Roman Province, Sovereign of the Vatican City State, Servant of the servants of God.
(This post is cobbled together from recollections confirmed by and many specifics I didn't know from various Wikipedia entries.)