Tullius was a Roman nomen

Roman naming conventions

By the Republican era and throughout the Imperial era, a name in ancient Rome for a male citizen consisted of three parts : praenomen , nomen and cognomen...

. The feminine form was Tullia. Tully

Tully

Tully is a surname of Irish origin. The surname itself and its variants include; Tally, MacTully, Tilly and Flood, all of which can derive from several different unrelated Irish families such as; Ó Maoltuile, Taithligh, Mac Maoltuile, Ó Taithligh, and Mac an Tuile...

, especially as another name for Cicero

Cicero

Marcus Tullius Cicero , was a Roman philosopher, statesman, lawyer, political theorist, and Roman constitutionalist. He came from a wealthy municipal family of the equestrian order, and is widely considered one of Rome's greatest orators and prose stylists.He introduced the Romans to the chief...

, is an anglicized form now considered antiquated.

Not all those who have the nomen are related by blood; Cicero himself did not believe that he was descended from Servius Tullius, though at one point he referred to their shared gens.

• Servius Tullius
  Servius Tullius
  Servius Tullius was the legendary sixth king of ancient Rome, and the second of its Etruscan dynasty. He reigned 578-535 BC. Roman and Greek sources describe his servile origins and later marriage to a daughter of Lucius Tarquinius Priscus, Rome's first Etruscan king, who was assassinated in 579 BC...
  
  , early king
• Manius Tullius Longus
  Manius Tullius Longus
  Manius Tullius Longus was consul at Rome in 500 BC, with Servius Sulpicius Camerinus Cornutus.Livius reports that no important events occurred during this year, but Dionysius states that a conspiracy to restore the Tarquins to power was detected and crushed by Camerinus. Tullius died during the...
  
  , consul
  Consul
  Consul was the highest elected office of the Roman Republic and an appointive office under the Empire. The title was also used in other city states and also revived in modern states, notably in the First French Republic...
  
   500 BC
• Marcus Tullius Decula
  Marcus Tullius Decula
  Marcus Tullius Decula was a consul of the Roman Republic in 81 BC, with Gnaeus Cornelius Dolabella, during the dictatorship of Sulla; but the consuls of that year were only nominal, as Sulla had all the power in his hands....
  
  , consul 81 BC
  81 BC
  Year 81 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Decula and Dolabella...
  
  
• Marcus Tullius Cicero (Cicero), consul and orator
• Marcus Tullius Tiro
  Marcus Tullius Tiro
  Marcus Tullius Tiro was first a slave, then a freedman of Cicero.The date of Tiro's birth is uncertain. From Jerome it can be dated to 103 BC, which would make him only a little younger than Cicero...
  
  , freedman of Cicero
• Quintus Tullius Cicero
  Quintus Tullius Cicero
  Quintus Tullius Cicero was the younger brother of the celebrated orator, philosopher and statesman Marcus Tullius Cicero. He was born into a family of the equestrian order, as the son of a wealthy landowner in Arpinum, some 100 kilometres south-east of Rome.- Biography :Cicero's well-to-do father...
  
  , one of Caesar's
  Julius Caesar
  Gaius Julius Caesar was a Roman general and statesman and a distinguished writer of Latin prose. He played a critical role in the gradual transformation of the Roman Republic into the Roman Empire....
  
   generals and younger brother of Marcus

The "Tullus" of the king Tullus Hostilius

Tullus Hostilius

Tullus Hostilius was the legendary third of the Kings of Rome. He succeeded Numa Pompilius, and was succeeded by Ancus Marcius...

 is a forename derived from the same root (compare the Roman praenomen

Praenomen

The praenomen was a personal name chosen by the parents of a Roman child. It was first bestowed on the dies lustricus , the eighth day after the birth of a girl, or the ninth day after the birth of a boy...

 Marcus with the nomen gentile Marcius). There is no genetic relationship implied.