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Everyone should know what the rock is. It isn't Peter.
I'm sure you've seen this post before, but evidently it needs repeating...

Grammatically speaking, petra in Mt16:18 cannot refer to anything but petros. (Citations used below are from the following reference works: (1) A Greek Grammar of the New Testament and Other Early Christian Literature, DeBrunner (tr. Funk), University of Chicago Press (“Grammar”); (2) A Greek-English Lexicon of the New Testament and Other Early Christian Literature, Arndt & Gingrich, University of Chicago Press (“Lexicon”))
1. petros
"Hellenization of Semitic personal names.... By translation." Cf. Jn1:42 – “you will be called Kephas, which means Peter.” (Grammar, 53(2e)). The name Peter is a Hellenization by translation of Kephas.

“The use of the article with personal names is varied; as a general rule ... the absence of the article merely names him.” (Lexicon, o, h, to, II.b.) Note that there is no article before petros in Mt16:18. In this part of the verse, Jesus is merely giving Peter his new name.
2. kai
“Epexegetical kai ... Emphatic with demonstrative ...” (Grammar 442/9.) Note the demonstrative adjective tauth, a contraction for th auth. So the sentence that follows kai is epexegetical of “You are Peter.” This epexegetical use of kai is reinforced by the following: “Kai with the future ... is used to denote a further result” (Grammar, 442(3)). Note the use of the future: “I will build my church”. The building of the church is a further result of the name change. (See also, Lexicon, kai, 3 ("Other explicative uses are kai tauto ... ").)
3. tauth.
o auto: An idiom composed of two words with one meaning: “same”. This word modifies petra. What same rock? There is only one other word in the verse with the base petr-, and that is petros. (Note: A Greek noun comprises two parts: a base that indicates basic meaning, and an ending that indicates grammatical gender (among other things). Although there is not necessarily a correspondence between a noun's grammatical gender and a thing's actual sex (e.g., petra is feminine gender, even though a rock is sexless), the gender of a personal name virtually always corresponds with the person’s sex (e.g., petros is masculine gender, just as Peter is a man).)
4. th:
"In its individualizing use it focuses attention on a single thing or concept as already known or more definitely limited: things and persons that are unique in kind. " (Lexicon, o, ei, to, II.a.) Thus, petra is preceded by the article th to indicate it is already known (compare with petros, above, which is not preceded by a definite article). Moreover, when combined with the demonstrative adjective tauth (same), the definite article becomes emphatic (the very same rock).
Summary: We know that petra refers to petros because (1) the demonstrative adjective and definite article that modify petra indicate that the identity of the rock is known; (2) petra and petros share the same base and thus the same basic meaning; and (3) the sentence following kai is epexegetical of the sentence that precedes kai, the further result being that Jesus will build his church on the very same rock.