The beloved Gaius refers to the addressee, not a group as in 2 John 1, but one individual.
For beloved see comments on 1 John 2.7; the next phrase, whom I love in the truth, shows that the use of this word may be more than a matter of merely traditional kindness or politeness.
Some renderings of the phrase used are “To my dear Gaius, whom I truly love” (Good News Translation), ‘To Gaius, my friend (or brother), who is very dear to me’; or in two sentences, ‘to Gaius whom I love. I love him/you with all my heart.’
The phrase does not contain a respectful term such as “lady” in 2 John 1. This implies that the level of language to be chosen may be of a more informal or intimate type than in John’s second Letter.
Gaius was a very common name. Consequently there is no reason to identify him with others of the name mentioned in the New Testament (Acts 19.29; 20.4; 1 Cor 1.14, compare Rom 16.23). He is presented in the Letter as a good friend of John’s. He was probably the center of a group of Christian friends, not necessarily an elder of a congregation.
For the other details in this verse, see comments on 2 John 1, which has the same function in the Letter.
Quoted with permission from Haas, C., de Jonge, M. and Swellengrebel, J.L. A Handbook on The Third Letter of John. (UBS Handbook Series). New York: UBS, 1972. For this and other handbooks for translators see here .