🔼The name Quartus in the Bible
The name Quartus occurs only once in the Bible. At his conclusion of Paul's letter to the Romans, Paul's scribe Tertius greets a number of people, among whom Quartus "the brother" (Romans 16:23). It's not clear why Quartus receives the epithet "brother" as we may assume that pretty much everybody Paul and Tertius mention are brothers and sisters. Some have proposed that Quartus is the brother of Erastus, but that would probably have warranted a different wording.
It's possible that Quartus was nicknamed The Brother because of some occupation, or perhaps to distinguish him from an unmentioned namesake Quartus The Cousin. Church tradition regards Quartus (as Quartus of Berytus) as one of the seventy disciples (Luke 10:1), but there's no Scriptural evidence of this.
🔼Etymology of the name Quartus
The name Quartus is the same as the off-the-shelf Latin adjective quartus, meaning the fourth, from quatrio, meaning four. Hebrew names that mean four are Arba and Reba, although in Hebrew it wasn't customary to name people after numbers, and the name Arba entails a lot more than a simple numeral.
The name Quartus means Fourth, and note that the name Tertius means Third. Naming people after numbers was quite common in Roman times. There are plenty men named Primus, Secundus and so on known in literature (the birth name of Caesar Augustus was Octavius, meaning Eighth), but perhaps it's of underestimated significance that the name of Brother Quartus (4th) occurs almost immediately after that of Tertius (3rd).