Well, it all makes sense when we realize that "Aristarchus" had received this name, which means "best ruler" (best Archon?) in recognition of his benefactions towards the church. By using the name "Aristarchus" (unabbreviated) in this letter, Paul reminds Philemon of Aristarchus's benefactions. Paul wants Philemon to be a benefactor (by releasing Onesimus), so the mention of Aristarchus provides Philemon with an example to follow (see my post on the purpose of the greetings here). It was Paul's style to use someone's new name to draw attention to the role for which the person was named. Thus Paul calls Cephas "Rock" in Gal 2:7-8 when discussing Cephas's role in the church. Similarly, Paul calls Gaius-Titius-Justus "Stephanas" in 1 Cor 1:16 and (more clearly) in 1 Cor 16:15-17 when his benefaction of his house and household are in view (see the discussion with Doug here). It is also possible that Paul calls Crispus "Sosthenes" at 1 Cor 1:1 for the same reason.
Benefactors in the church often received new names. The strongest evidence is for the case of Crispus-Sosthenes, but I have also argued for Stephanas. Other examples include Joseph-Barnabas (Acts 4:36-37) and probably Mary Magdalene.
Aristarchus was one of those who was chosen to accompany the collection to Jerusalem (Acts 20:4). Philo, referring to the temple tax, wrote,
At stated times there are appointed to carry the sacred tribute envoys selected on their merits, from every city those of the highest repute, under whose conduct the hopes of each and all will travel safely. (De spec. leg. I, xiv, 78)It is therefore likely that Aristarchus was of high repute and trusted with money. The names in Acts 20:4 are ordered geographically, but Aristarchus is named before the other Thessalonian (Secundus). All this fits nicely with the proposal that he was a respected benefactor who was worthy of the name "Aristarchus".
All this is supported by the fact that Aristarchus has a doppelganger in the person of Jason. Let us explore whether Jason was given the name "Aristarchus". Jason is the only other benefactor of the Thessalonian church that we know about (Acts 17:5-9). He appears again in Rom 16:21. From this verse, his name, and his early conversion, we deduce that he was probably a Jew. Colossians 4:10-11 suggests that Aristarchus was also a Jew. This is supported by (Acts 27:2) which shows that Aristarchus had been in Caesarea. Also, the charge against Paul was that he had been too supportive of the rights of Gentiles, so it would not have done Paul's case any good if his helpers (Aristarchus and the author of Acts) were Gentiles. In Acts 21:40-22:3, for example, he defends himself by appealing to his won Jewishness, and in Acts 22:12-14 he emphasizes the Jewishness of his supporter, Ananias (see my discussion here). He would therefore have wanted Jewish helpers. That both Jason and Aristarchus were probably Jews is significant since the church of Thessalonica was mainly Gentile (see 1 Thess).
We learn, more importantly, from Rom 16:21, that Jason was in Corinth just before Paul left their with the collection delegates, including Aristarchus. Jason is mentioned third out of 8 greeters, and is in a group with Timothy, Lucius and Sosipater. Timothy was one of those who accompanied the collection, and so was Sosipater/Sopater, and in my next post I will start to build the case that Lucius was too. It is therefore likely, as some commentators point out, that Jason also accompanied the collection. This supports the Jason=Aristarchus equation, for Acts 20:4 lists Paul's travel companions and mentions "Aristarchus" where we would expect Jason to be mentioned.
We must still explain the name selections. I have suggested why Paul calls him "Aristarchus" in Philemon 24, and it makes sense that he calls him "Jason" at Rom 16:21, since the Christians in Rome would not have understood the significance of the name "Aristarchus" (compare "Gaius" in Rom 16:23). But why would Acts call him "Jason" at Acts 17:5-9, but "Aristarchus" at Acts 19:29 and Acts 27:2? Why doesn't Acts explicitly equate them? Doesn't this argument from silence suggest that we are looking at two people after all? I suggest that this is a protective silence. Roman informers and other opponents of the church might get access to a copy of Acts, so Luke was careful not to give away sensitive information. He therefore avoided any hint that the Christians defied civil authorities. So he makes no further mention of "Jason", lest anyone think that Jason broke the terms of his bail (which may have been the case), and he does not reveal that Jason took an alias (which may have been viewed with suspicion). Luke's informed readers would have understood the references to Jason and Aristarchus, but opponents would have been kept in the dark. Luke's silence about the identity of Sosthenes, and his silence about the collection can be similarly explained (see here and here). Arguments from silence do not work with Acts when the civil authorities are close at hand.
In summary, I propose that Jason, a Jew, and the founding benefactor of the church of Thessalonica, was given the name/title "Aristarchus" (best ruler). His new name was appropriately used unabbreviated in Paul's letter to Philemon. He arrived in Corinth (Rom 16:21), having been selected, as we might expect, to traveled with Paul to Jerusalem (Acts 20:4) with the collection.