before winter: Paul probably worried about a long delay if Timothy missed the chance to travel in the fall (see 1:4; 4:9). Winter weather interrupted travel across the Adriatic Sea from November to March (see Acts 27:12). Paul might also have been eager to receive his cloak for the cold prison (2 Timothy 4:13). The New Testament does not mention Eubulus elsewhere. But he was obviously well-known to Timothy.
Pudens was a name used by upper-class families.
Linus: Both the bishop Eusebius and the bishop Irenaeus later identified Linus as the first bishop of Rome.
The New Testament does not mention Claudia elsewhere.
brothers: Greek adelphoi, a term for family members, both male and female.