These two letters name-drop quite a few random Christians. Even though these guys and gals were obviously pretty noteworthy back in their day, they've sort of fallen off the map since then. Let's take some time and give them their limelight back.
Paul calls him out as the co-author in his letter to the Colossians. Hey, we all know Paul was running the show, but it's nice to get some recognition. Timothy is a name you'll hear a lot if you sort through Paul's letters. The two guys first meet in Acts 16, where Timothy is called a "disciple" and Paul arranges for him to be circumcised. Well, that's a fine how-do-you-do.
Throughout their lives, Paul probably functioned as kind of a mentor for Timothy. He sends him all around the Roman Empire visiting various churches. He praises Timothy repeatedly saying, "I have no one like him" and that the kid is like "a son" (Philippians 2:20, 22). He also shows up in Romans, 1 & 2 Corinthians, 1 & 2 Thessalonians, Philemon, and Hebrews. Timmy even had two books of the Bible named after him: The First and Second Epistles to Timothy. He's kind of like the Where's Waldo of the Bible. He keeps popping up everywhere if you know where to look.
Though he only gets a couple mentions, Epaphras is kind of a big deal. When Paul writes to the Colossians, he says they "learned from Epaphras, our beloved fellow servant" (Colossians 1:7). He also reports back to Paul with how the community is doing and makes "known to [Paul their] love in the Spirit." Paul also praises him for his hard work and constant prayers for the Colossians (Colossians 4:12-13).
Basically, it looks like Epaphras is the founder of the church in Colossae. Sadly, things don't seem to be looking up for him in Paul's other letters. In his letter to Philemon, Paul calls Epaphras "a fellow prisoner" (Philemon 1:23). Tough luck, pal.
This name comes up in both Ephesians and Colossians. Paul says that he's sending Tychicus—"a dear brother and a faithful minister" (Ephesians 6:21)—to let the folks in Ephesus know what's going on with him. In Colossians, he gets pretty much the same job and is called "a beloved brother, a faithful minister, and a fellow servant" (Colossians 4:7). Sounds like a stand-up guy.
According to Acts, Tychicus was one of Paul's traveling companions. He went to Macedonia with him (Acts 20:4) and the author says that he's from Asia, which was around the area where Ephesus was. Tychicus is also mentioned in 2 Timothy—he comes to relieve Tim of duty in Ephesus (2 Timothy 4:12). Paul also has him go to see Titus later, too (Titus 3:12). He really got around.
Paul really briefly mentions this guy by saying that he's coming to Colossae with Tychicus and by calling him a "faithful and beloved brother, who is one of you" (Colossians 4:9). But Onesimus has a much bigger role to play in another book of the Bible.
Paul's letter to Philemon is written all about Onesimus who is actually Philemon's slave. Apparently, Onesimus met up with Paul in prison and, after talking to Paul, decided to convert to Christianity. Paul called Onesimus "my child" and "my own heart" (Philemon 1:10, 12), so they'd gotten pretty tight behind bars.
In the letter, Paul is super concerned with how masters and slaves who both happen to be Christians should treat each other. Paul encourages Philemon to welcome Onesimus "no longer as a slave but more than a slave—a beloved brother" (Philemon 1:15). No one knows exactly how things worked out for Onesimus, but it looks like he did find a new way to be of use to Paul in Colossae.
Paul calls this guy out as a "fellow prisoner" (Colossians 4:10). He's also a fellow Jew. Elsewhere in the Bible, Aristarchus from Thessalonica traveled far and wide with Paul. Guess that's how he wound up behind bars.
It's sort of a bummer to be remembered as someone's cousin for all eternity, but Barnabas was one of Paul's closest friends, so we'll forgive him. Mark is there when Paul is writing from prison so he passes along his greetings to his friends (Colossians 4:10). He sometimes gets confused with John Mark, who Paul did not want to bring along on one of his missionary trips with Barnabas (Acts 15:39) and Mark the author of the gospel. Sure, they might be the same guys…or this might just be good ol' cousin Mark hanging out.
This dude was a fellow Jew hanging out with Paul when he wrote his letter to the Colossians. You might be wondering how this guy got to share the same name as the Savior of the World. It's really just a coincidence. The name Jesus is just a Greek version of the Hebrew name Yeshua or Joshua. Since Joshua was a big hero in the Hebrew Bible, the name was a pretty popular boys name in Jewish circles. We bet the nickname came in handy for clearing up any confusion between the two.
Paul just says that "Luke, the beloved physician" (Colossians 4:14) sends his best wishes. Does he mean Luke? As in the Gospel of Luke?
Church tradition says that Luke wrote both his gospel and Acts and that he was also a doctor (which comes right from this passage). Paul also mentions him in Philemon 1:24 and 2 Timothy 4:11 (which Paul almost certainly didn't write). So, no, it's probably not the same guy, but it's kind of a cool shout-out anyway.
Demas is just sort of hanging around, sending greetings, and not doing anything much. His name also comes up in Philemon 1:24 and 2 Timothy 4:10, where the author accuses Demas of being "in love with this present world" and deserting him to leave for Thessalonica. Bummer, Demas. Bummer.
This lovely lady hosts church services in her home in Laodicea, which Paul is very grateful for (Colossians 4:15). Of course, he never mentions her again in any of his other letters, but still. Folks who hosted house churches were usually wealthy, so Nympha could be an important member of the community and a leading lady. We wonder what she thought of Paul's advice to wives to obey their husbands?
Paul reminds Archippus to "complete the task that [he has] received in the Lord" (Colossians 4:17). But what is it? Oh, mysteries. This name also pops up as one of the people who the letter to Philemon is addressed to (Philemon 1:2). Legend has it that Archippus could have actually been Philemon's son. Wonder what he thought of his dad owning slaves?