See Poole on "1 Timothy 1:2"; there he calls him his own son, testifying his relation, here his beloved son, to testify his affection to him. The salutation is the same with that in 1 Timothy 1:2.
Related Commentaries of 2 Timothy 1:2
2 Timothy 1:2
2 To Timothy, my dearly beloved son: Grace, mercy, and peace, from God the Father and Christ Jesus our Lord.