What is the name of the Filipino martial art?

Kali/Escrima/Arnis (different names for the same martial art) was developed in the Phillipines. It is a style that involves using a particular sort of hanbo (quarterstaff) that is light but sturdy. There are also techniques for use of two hanbo (one in each hand) and some limited empty-handed techniques (presumably that entail disarming/taking the opponent's hanbo).

This style is reasonably easy to find in major US cities, and is popular as a sport.

If you are looking for an exotic hand-to-hand style from roughly the same region, Indonesia is the birthplace of Pentjak-Silat (or Pencack-Silat), which is very aggressive.