I have the opposite opinion - which only demonstrates that this isn't straightforward!
I would treat his name and the identity of his father as two separate issues.
So I would record the LNAB as Pearce, because this was his legal name for the first few months of his life.
His current name would be whichever spelling of Tedeschi he used for the rest of his life, and the other spelling could go in the other names field, if you think it needs to be there.
Who his father was is a different question, and I would attach him as Albert Tedeschi's son, but with the full explanation you've given here in the bio.