As Jesus and his disciples approach Jerusalem, a rich man asks Jesus about eternal life (19:16). Specifically, the rich man asks Jesus if there is a good deed he must do in order to be right with God and enter the kingdom of heaven.
Who is this rich man? Mark 10:13 simply called him a man, Matthew 19:22 adds that he was young, Luke 18:18 says he was a ruler (ἄρχων) who was “extremely rich” (πλούσιος σφόδρα; 18:23). In Matthew 8:19 a scribe came up to Jesus, using similar vocabulary and syntax (εἷς προσελθὼν αὐτῷ εἶπεν). If he is a scribe and an official in the bureaucracy of Jerusalem, then he would be wealthy. Young and wealthy may imply he was from a good family which accumulated wealth and power in Jerusalem. Wealth was a sign of God’s blessing based on the blessings in the Law for those who are obedient. The man might think he is right with God because his family has been materially blessed.
Is this rich man the young rabbi Saul? Stanley Porter examines Paul’s words in 1 Corinthians 9:1, “Have I not seen Jesus our Lord?” and argues Paul knew Jesus before the Road to Damascus (When Paul Met Jesus: How an Idea Got Lost in History [Cambridge, 2016]; see my review here). Porter offers a detailed exegesis of this passage, comparing it to 1 Corinthians 15:1-11 to argue that Paul had seen Jesus just as the other apostles had. He is careful to suggest this as a possible reading of the text, but along with 1 Corinthians 9:1 and the book of Acts, there is a strong possibility Paul had known Jesus prior to his conversion experience. He very tentatively suggests Paul was the “the lawyer who asked the question” in Luke 10:25-28 (147). Similarly, that Paul “overheard Jesus’ words regarding the worker being worthy of his/her wages” (159) seems to go beyond the evidence or that Paul overheard the Olivet Discourse and “heard enough” of Jesus at that point (167). All of these are of course possibilities but move into the area of speculation which cannot be supported by evidence.
The man asks what good thing he needs to do to have eternal life (v. 16). If he was extremely wealthy, he might want to know what public benefit he must do to assure his place in the kingdom of heaven.
We cannot know any details about the man other than he sincerely wanted to hear Jesus’s opinion on what kind of good deed he needed to do to guarantee eternal life.