I'm not sure exactly what you're claiming the data show very clearly, but I'm pretty sure it's not the same thing as what your significance test shows.
The null hypothesis of your significance test is:<blockquote>The guesses are independent and, for each guess, the probability that it's a 'J' is equal to the relative frequency of 'J' names in the general population.</blockquote>You've provided evidence against this null hypothesis. You've provided no evidence against the claim that the only thing wrong with the null hypothesis is the assumption of independence. Doing that would require a different significance test.
(What is the point of this whole discussion anyway? I guess some participants or lurkers might increase their understanding of statistics, so it's not entirely pointless. I doubt a significance test with a p-value of 1/20 or so will change anyone's mind either way about the existence of souls; nor should it, really, if their prior opinion was based on more evidence than that.)