As a denizen of the first century Greco-Roman world and as a popular teacher that would have been increasingly viewed through messianic lenses, Jesus would have been quite conscientious of the way that He was perceived by the public. That said, He appears to be almost completely unconcerned with the honor and shame system. It almost seems as if He viewed it as being quite backwards, with actions seen as most honorable by the wider public, perceived by Jesus as being shameful, and vice versa.
At times, Jesus accepts the honors being afforded to Him, but generally He only accepts honoring or honorific statements when they come from those that do not possess any public honor (tax collectors, lepers, those that have been possessed by demons, unclean women, etc…). When the rich or the rulers attempt to honor Him (and thus flatter themselves and attempt to accrue honor by their own association with Him), perhaps by calling Him “good,” He disavows the approbation. He routinely speaks of the first being last and the last being first. He interacts with tax collectors, who may have money and a measure of power, but who are not looked upon as being honorable in the least. He touches lepers. He allows dishonorable women to touch Him.
He is more than happy to take the lowest place at a meal, eschewing the places of honor and instructing His followers to do the same. He washes the feet of His disciples, which is the role of a slave and a reminder of the slave’s shameful place. He allows children who, being children, do not have a place in the honor and shame pursuit (they do not have honor or shame accorded to them), to come to Him. When they do, He tells those who are listening to Him that they must enter the kingdom of Israel’s God as little children---unconcerned with the pursuit of honor or the avoidance of shame (which has nothing to do with a “childlike faith”). He ultimately ended up on a cross, which was the lowest and most shameful place of all, and He went there willingly as He embraced the role of Israel for the world.
These things (the honor and shame culture along with Jesus’ treatment of this broad social construct) would have been well understood by Jesus’ followers and those that made up the believing communities that attempted to live out what it meant to be the renewed Israel that represented the rule of the Creator God through the remembrance of and reflection upon the orally transmitted Jesus tradition. When Paul wrote his letters, especially what are considered to be the early letters, there were at that point no known and codified written record of the life of Jesus. There were no Gospels of Matthew, Mark, Luke, and John as they exist in their present form. Paul doesn’t have his own body of work or the letters from other apostles from which to draw, nor do the early believers. What they had were the words of the apostles.
Those apostles shared their stories of Jesus (a relatively unified story to be sure, though with different emphases, as is obvious from the variety of presentations of the life of Jesus that can be seen in the Gospels) so that those who threw in their lot with the crucified and resurrected King (the church) might do their best to model out the example that He provided, as the movement of the kingdom of the Creator God began to spread through the world via the instrument of the church, with this spread understood to have been motivated by the Spirit of God. They too were to be motivated to eschew honor and embrace shame, especially if such brought glory to their King and to their God and extended the reach and rule of that Kingdom as they conscientiously strived to bring heaven to earth by mimicking the counter-cultural behavior of Jesus.