Based on the Comic Book by Budjette Tan and Kajo Baldissimo
Anton Trese's two Sigbin bodyguards are named "Puti" (White) and "Bantay" (Guard). They're very common pet dog names in the Philippines, akin to "Spot" or "Rover".
Twins who are sidekicks of Trese are named after characters in Noli Me Tangere: Crispin and Basilyo.
Trese literally means 13 (thirteen) which is very fitting because 13 is always related to supernatural things.
Oliva tried to balance out the Trese animated series to satisfy the existing fan-base and those who were not familiar with the original source material. He intended to retain the source material's central theme of "family and duty" which he describe are "universal ideas and very Filipino".