Heidegger's Bible Handbook: 2 Corinthians: Authorship
2. Why would Saint Paul join Timothy to himself in the inscription?

Saint Paul, the author of the Epistle, in the inscription joins Τιμόθεος ὁ ἀδελφός, Timothy our brother, with himself, 2 Corinthians 1:1; which he also does in other Epistles, namely, Philippians, Colossians, and Thessalonians; not because he is an assistant to Paul in the composition of the Epistle: but both for the sake of honor, and so that he might bear witness to his accord with him.