how did it get the name?
The root is found in the Latin praenomen "Tiberius".
Tiber
It is probable that the genesis of the name "Tiber" was pre-Latin, like the Roman name of Tibur (modern Tivoli), and may be specifically Italic in origin. The same root is found in the Latin praenomen "Tiberius". 
what was the most powerful lawmaking body in the roman republic Assemblies how many types of assemblies are there? Curiate Assembly, the Centuriate Assembly, and the Tribal Assembly. what is the role of the extraordinary magistrates? The dictator of the extraordinary magistrates had "maius imperium" and total authority to command the state; however, since the dictator generally tried to maintain order, this did not conflict with the responsibilities of the other magistrates, who continued to function during a dictatorship. what is the function of the first assembly? It was ethnic in nature, and thus were organized on the basis of the early Roman family, or, more specifically, on the basis of the thirty original patrician (aristocratic) clans. who formed the roman constitution? It emerged from that of the Roman kingdom. what regions come under this kingdom? Tiber, Palatine Hill and hills surrounding it. what is the first mentioned one? The third-longest river in Italy.
wiki:19647737
Tiber [SEP] Etymology
It is probable that the genesis of the name "Tiber" was pre-Latin, like the Roman name of Tibur (modern Tivoli), and may be specifically Italic in origin. The same root is found in the Latin praenomen "Tiberius". There are also Etruscan variants of this praenomen in "Thefarie" (borrowed from Faliscan "*Tiferios", lit. '(He) from the Tiber' < "*Tiferis" 'Tiber') and "Teperie" (via the Latin hydronym "Tiber"). The legendary king Tiberinus, ninth in the king-list of Alba Longa, was said to have drowned in the river Albula, which was afterward called "Tiberis". The myth may have explained a memory of an earlier, perhaps pre-Indo-European name for the river, "white" ("alba") with sediment, or "from the mountains" from pre-Indo-European word "alba, albion" mount, elevated area.