Since Crispus was an early convert (1 Cor 1:14), Sosthenes also seems a believer (1:1), and both are described by Luke as "synagogue rulers" (Acts 18:8, 17), it is possible that these are two names for the same person (allowing frustrated members of the synagogue community to beat their former leader Crispus in 18:17). This proposal is ultimately unlikely, however; why would Luke change names without an explanation connecting them? (That Paul likewise uses both names reinforces the objection.)Keener here considers the Crispus-Sosthenes hypothesis but raises the superficial objection that Luke does not explicitly identify them. In this post I will answer Keener's objection using his own observations.
If Luke expected his readers to already know that Sosthenes was Crispus then he would have no reason to state the fact. Keener argues that the audience of Acts already knew James (2241), Jason (2533, 2549), probably Alexander (2869) and possibly Tyrannus (2829). Indeed, he believes that Sosthenes was known to Luke (2779). It is therefore odd that Keener does not explore the possibility that the audience of Acts knew Crispus-Sosthenes. The little that we know about him suggests that he may well have become well known throughout the Aegean churches. He was the synagogue ruler and therefore high status. Many in Corinth had come to the faith under his influence (Acts 18:8), and his name, "Sosthenes" (saving strength), reminded everyone that Paul had honoured him for the part that he had played in the formation of the church. He was so well respected in Corinth that Paul cited his endorsement of the contents of 1 Corinthians (1 Cor 1:1). He had been with Paul in Corinth for 18 months and in Ephesus for perhaps 2 years. We know of no other person in the Aegean region who had spend more time with Paul. He had the wealth to travel among the Aegean churches and his fame would have been spread by 1 Corinthians itself when the letter was copied. It is not at all surprising that Luke's audience, which was likely the Aegean churches (see here and here), knew Crispus-Sosthenes.
There is also a good reason why Luke would have wanted to avoid explicitly identifying Sosthenes as Crispus. Throughout his commentary Keener is acutely aware of the fact that Luke presented the faith as unthreatening to Rome. Indeed, on Acts 18:12-17 he writes,
Although Gallio as an actor within the narrative was not trying to provide an apologetic for Paul or his movement, this is de facto how his response functions in the larger context of Acts' apologetic. As soon as a governor's verdict was read out, it was recorded in the province's official proceedings. Because he was a governor and not a local judge (like Thessalonica's politarchs, Acts 17:6-8), Gallio's decision could have far-reaching implications. It would establish a favorable precedent for the Christians .... Luke's marshaling of such precedents would provide Christians with a sense of security and perhaps evidence they could use to respond against slanders in the public arena. (2773-4)If Luke had explicitly equated Sosthenes with Crispus the text would not have provided the Christians with such a positive precedent that they could bring before Roman officials. Gallio had allowed the Jews to beat a Christian benefactor and this is hardly the kind of precedent that Luke wanted to publicize. Luke's purposes were served by his silence about the identity of Sosthenes.
Keener also objects that 1 Cor 1:1 calls him "Sosthenes", whereas Cor 1:14 calls him "Crispus". However, in 1 Cor 1:1 Paul is appealing to the authority of Sosthenes so it unsurprising that he should use the name that honoured him. In 1 Cor 1:14 Paul is wanting to avoid any hint that being baptized by him is a point of honour, and perhaps for that reason he uses his ordinary name, "Crispus". In any case, 1 Cor 1:14 refers to a time before Crispus was given the name "Sosthenes".
Finally, Keener makes a point that supports the Crispus-Sosthenes hypothesis:
We know of food shortages close to 51C.E., and these often contributed to instability ... The schism in the Jewish community had, among other things, caused rancour and divided the community's patrons and resources at a time when it could ill afford the division (after Claudius's expulsion in 18:2). (2765)This economic hardship explains why the Jews beat their benefactor, who had defected to the Christians.