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The authority of the Church is not based solely on the renaming of Peter episode, but also, and, in fact, primarily on

15 But if thy brother shall offend against thee, go, and rebuke him between thee and him alone. If he shall hear thee, thou shalt gain thy brother. 16 And if he will not hear thee, take with thee one or two more: that in the mouth of two or three witnesses every word may stand. 17 And if he will not hear them: tell the church. And if he will not hear the church, let him be to thee as the heathen and publican. 18 Amen I say to you, whatsoever you shall bind upon earth, shall be bound also in heaven; and whatsoever you shall loose upon earth, shall be loosed also in heaven
(Mt 18)

The unique authority of Peter is, of course, evident in several gospel episodes beside the renaming; he is promised the keys to the Kingdom of Heaven and the power to bind and loose is first given him; Christ promises to pray for him personally at the Last Supper so that he, Peter, may not fail and convert his brethren; Peter is charged with feeding Christ's sheep; Peter converts the first Gentile and it is his vision that makes a clean break with the Jewish ceremonial and dietetic law.

But what about the renaming episode? You acknowledge that the actual conversation takes place in Aramaic and is not recorded at all, so we are dealing with the limitations of the Greek translation. The patristic Greek has only feminine for "rock", "petra"; the diminutive "petros" is not recorded in the Koine Greek. So, St. Matthew had to fit the feminine "petra" into the masculine name, so he writes "petros". Naturally, the pronouns have to agree with the word they point to and the grammar of the phrase (like in any language), so since Jesus is talking to Peter about a rock (and not to a rock about Peter), the pronouns are "thou" (soi) and "this" (taute te).

This is really a first, rejecting the scripture for being too grammatical, then calling the normative interpretation "ungrammatical - take a cigar.

The authority of the Church is not based solely on the renaming of Peter episode, but also, and, in fact, primarily on... (Mt 18)

Where is it stated that this is only to Peter?

Consider Matthew 18:18-20

“Assuredly, I say to you, whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven. “Again I say to you that if two of you agree on earth concerning anything that they ask, it will be done for them by My Father in heaven. For where two or three are gathered together in My name, I am there in the midst of them.”

That doesn't sound exclusive to Peter. And you bind and loose using keys...

But what about the renaming episode?

Peter is the first who showed faith saying Jesus is God, and is granted the name as an echo of Jesus (the rock) as we are all in calling ourselves Christians (little Christs). The foundation is Christ, and the Church is built though belief as Peter showed in Matt. 16.