1300-hastigiri-aNNan-vaDakalainess

was it the original Annan or his son/grandson who became tk? Latter is more possible.

Also, the title PB originally belonged to Swami Desikan as seen from the colophon of sindhumativilasa written by Gopanarya, Swami’s sishya. So KV gave the title of his father to PB swami.