If you type “the naked public square” into Google, 0.41 seconds later you get access to 252,000 entries. My guess is that this greatly underestimates the number of times that this phrase has been quoted and the number of people it has influenced. Even so it confers immortality of a kind on whoever happened to coin it. According to Wikipedia, that person was Fr. Richard John Neuhaus, who, while still a Lutheran pastor, wrote a 1984 book of that name arguing that the extreme secularist interpretation of the First Amendment had already led to the effective exclusion of religious argument from political debate and would in time foster an official hostility to religion that the First Amendment was written to prevent. In fact there are uses of the phrase earlier, some from Neuhaus himself, others by friends of his such as Irving Kristol. So it is likely that he coined it, but certain that he gave it common currency.
To achieve immortality as the author of a telling phrase might have mildly pleased Neuhaus, who was not without a justified pride in his writing, but it was not the sort of immortality in which he was really interested. Two of his most important books, Death on a Friday Afternoon and As I Lay Dying, deal both intimately and powerfully with the certainty that we will all die and hopefully with the promise that we will all enjoy a literal immortality thereafter.