Why is the monetary unit of the Philippine called peso?

The simple answer is that it used to be a colony of Spain and used the Spanish monetary unit which is the Peso as well.

In the early 1900's the U.S.A. took control of the Philippines and established the unit of currency as a "gold peso" which was supposed to be 1/2 the value of a U.S. Dollar.

The Japanese occupied for a while as well, but the Peso has stuck as the monetary unit