The name Gaius (Γάϊος, Caius), which were a common Roman name, were mentioned five times in the New Testament, of three or four men.

1. In  1 Corinthians 1:14, a member of the Church of Corinth, baptized by St. Paul, who points out that in his case, as in the case of Crispus and in that of ‘the household of Stephanas,’ he thus deviated from his usual practice. Crispus was ‘the ruler of the synagogue’ ( Acts 18:8), and Gaius was presumably also a convert of some importance.

2. In  Romans 16:23, a member of the Church of Corinth, whom St. Paul in the postscript to Romans calls his ‘host’ and the host of ‘the whole church,’ and whoso salutations are sent to the readers of the letter. He was evidently a man of position and means (the greeting from him immediately precedes that from Erastus, ‘the treasurer of the city’), whether his hospitality took the form of keeping open house for Christians and Christian visitors like the Apostle at Corinth or of allowing the Christians to meet for common worship and edification under his roof.

Everything points to the identification of and 2. The same Gaius who was converted and baptized on St. Paul’s first visit to Corinth entertained him on his second visit. Now it is perhaps easier to believe that this Corinthian would have friends, whom he would wish to salute, at Ephesus rather than at Rome, and these salutations in  Romans 16:23 are thought by some scholars to point to an Ephesian destination of the passage. But as Lightfoot remarks, in the Apostolic Church personal acquaintance was not necessary to create Christian sympathy ( Biblical Essays , 1893, p. 305).

3. In  Acts 19:29, a companion of St. Paul, who with Aristarchus was seized at Ephesus. They are described as ‘men of Macedonia’ (Μακεδόνας), there being very little support for another reading, ‘a man of Macedonia,’ referring to Aristarchus only.

4. In  Acts 20:4, a companion of St. Paul, who accompanied him from Greece to Asia Minor. He is described as ‘of Derbe’ (Δερβαῖος), possibly intentionally to distinguish him from 3.

Attempts have been made to identify and 4. It is natural to do so, as the passages stand so close together. Emendations of the text have been suggested by which ‘of Derbe’ is taken with ‘Timothy,’ but these are purely conjectural, and Timothy was apparently a Lystran ( Acts 16:1-2). See W. M. Ramsay, St. Paul the Traveller and the Roman Citizen , 1895, p. 280.

5. In  3 John 1:1, the person to whom 3 John is addressed. He is described as ‘the beloved’ (ὁ ἀγαπητός), and is commended for his hospitality (v. 5). Nothing is known of this Gaius, and there is no reason to suppose him to have been any one of those of the same name associated with St. Paul.

Hastings’ Dictionary of the New Testament