Does Peter's name suggest papal authority?

Catholics sometimes make claims like the ones I came across in a recent discussion about the papacy: "He spoke to Peter first, and changed his name and gave him the authority specifically. At no other point does God change someone's name and it does not denote new authority and responsibility."

Being spoken to first doesn't imply greater authority, and "new authority and responsibility" is too vague to lead us to papal authority and responsibility in particular. But what I want to focus on here is the issue of being given a new name.

It wasn't a name change. It was the giving of an additional name. In fact, Jesus referred to him as Simon more often than Peter, probably for a reason I've discussed elsewhere.

The new name was given prior to the time of Matthew 16 (John 1:42). It made sense for Jesus to adapt his choice of imagery to Peter's name in Matthew 16, but it doesn't follow that he was given the name primarily because of the context of Matthew 16. Even if he was given the name primarily or solely due to the Matthew 16 context, a papacy doesn't follow.

Other apostles were given a new name without any papacy involved or any other office unique to them that we're aware of (Mark 3:17). Thomas was given another name, but we don't know whether it came from Jesus (John 11:16). Peter wasn't even the only apostolic Simon who got a new name. Another apostolic Simon got one as well (Luke 6:15), though we, again, don't know whether it came from Jesus. None of these other apostles who were given another name are thought to be Popes or to have been given any other sort of church office in connection with the additional name.

Does the nature of Peter's new name suggest papal authority, even though the receiving of a new name doesn't? In the abstract, no. Being called a rock could involve papal authority, but that implication can't be shown to be probable. Similarly, given the associations between thunder and power, James and John's being called sons of thunder could be a reference to an office of authority (or a reference to their being bodily assumed to heaven in Revelation 11:19, if we want to speculate the way Catholics often do in another context), but such an implication can't be shown to be probable. And we don't just have abstract considerations to go by. Other passages refer to other apostles (Galatians 2:9, Ephesians 2:20, Revelation 21:14) or believers in general (Revelation 3:12) with the same or a similar concept as what's involved in Peter's name. Those other figures aren't thought to be Popes.

Much the same can be said about the singling out of Peter. In the abstract, his being singled out in Matthew 16 doesn't imply papal authority. A plausible, and overall better, alternative explanation of his being singled out is that he singled himself out by responding to Jesus' question. It wouldn't have made sense for Jesus to respond to Peter by talking to Philip. When Matthew 20:20-23 mentions James and John without mentioning the other apostles, we don't conclude that those two apostles had more authority than the others. The singling out of Philip in John 6:5 doesn't imply papal authority. When Acts 9:1-19 focuses on Paul and refers to various things that happened to him or were said about him that didn't happen to and weren't said about the other apostles, we don't conclude that he had more authority than the other apostles. When Galatians 2:9 mentions three of the apostles without mentioning the others, we don't conclude that those three had more authority than the others. When Revelation 21:14 mentions the Twelve without mentioning Paul, we don't conclude that the Twelve had more authority than Paul.