Paul is referring to the time of Moses in the book of Exodus when Israel fled through the Red Sea as the Egyptian army pursued them. The word "our" refers to himself and the Corinthians and is inclusive. (See: [[rc://en/ta/man/translate/figs-inclusive]])
The "rock" was a literal, physical rock, so it would be best to translate this literally. If your language cannot say that a rock "was" a person's name, treat the word "rock" as a metonym for the power of Christ that worked through the rock. AT: "it was Christ who worked through that rock" (See: [[rc://en/ta/man/translate/figs-metonymy]])