Albert Barnes on Philippians 4:21

Salute every saint in Christ Jesus. It was usual for him also to close his epistles with affectionate salutations to various members of the churches to which he wrote. These salutations are generally specific, and mention the names, particularly if prominent members of the churches. See the close of the epistles to the Romans; 1Corinthians; Colossians; and 2 Timothy. In this epistle, however, as in some others, the salutation is general. Why none are specified in particular is not certainly known.

The brethren which are with me, etc. The word "brethren" here probably refers to ministers that were with Paul, as the "saints" in general are mentioned in the next verse. It is possible that at Rome the ministers were known by the general name of the brethren. --Pierce.