In addition to giving Peter a threefold chance to reaffirm his loyalty, Jesus’ threefold questioning of Peter was a relatively mild public rebuke for Peter’s threefold denial of Christ. The choice of names was fitting as a part of that rebuke. Surely you don’t suggest that Jesus, the Son of the Living God, “changed His mind” regarding the choice of names? Anyway, notice what He says: “Feed my lambs. Feed my sheep.” A singular responsibility not directed at any of the other Apostles. Not that they didn’t share the responsibility, but Peter (or, “Simon, son of John” if you insist, it doesn’t alter his authority) is charged with the task in a special way, overarching the others’ responsibilities.