In a French grammar I read that y can only replace nouns that are not proper nouns.
Thus, if I want to say Je pense à ce problème, I can say J'y pense.
But if I want to say Je pense à Paul, apparently I cannot say J'y pense.
Is this accurate?
I don't think there is an issue with proper nouns per se but with people (Je vais en Belgique, J'y vais has no issue at all for me, while Je pense à mon cousin, j'y pense has the same feeling as with Paul).
According to Grevisse, y can refer to people when used as indirect object because in some cases lui and similar pronouns are not an option; or, in a more literary language, it can be used for other kinds of complements. But all the given examples feel either literary or popular to me (especially when nothing prevents the use of lui, or similar).
So I wonder if the language isn't losing the possibility to refer to a person with y and Grevisse described an intermediate state of an evolution which isn't stabilized yet (Grevisse notes that it occurred far more often in the past).
BTW The same holds for en.
Un francophone's answer is already good. Let's just mention the existence of this usage (y for personal pronoun) in popular speak, which would be flagged as incorrect in formal or professional context but still exists.
There are lots of examples in Renaud or Coluche texts: