🔼The name Phicol in the Bible
There are possibly two but probably only one man named Phicol in the Bible. He is the commander of the army of Abimelech of Gerar, and he and Abimelech travel to Abraham to make a peace pact with him (Genesis 21:22). That pact results in the naming of Beersheba (Genesis 21:31).
It was long assumed that there were two Abimelechs, who just happened to be named the same, but then there would also have to be two Phicols. But life spans during the age of the patriarchs were still about twice or three times the human life span of today, and there is no real valid objection to the conclusion that Abimelech and Phicol simply lived that long.
There are also scholars who believe that Abimelech is a royal title in stead of a personal name (comparable to Caesar or Pharaoh), and perhaps the "name" Phicol isn't a name either but the Philistine title of army commander.
🔼Etymology of the name Phicol
The name Phicol looks like it's a compound of two elements. The first part looks like it comes from the word פה (peh) or פי (pi), meaning mouth:
The second part of our name looks like the word כל (kol), meaning all or whole, from the verb כלה (kala), meaning to bring to completion:
For a meaning of the name Phicol, Jones' Dictionary of Old Testament Proper Names reads Mouth Of All, and explains this by stating that Phicol served as the spokesperson of the king, "the all".
The name Phicol certainly resembles the Hebrew for "mouth of all", but strictly etymologically this is probably dubious since neither NOBSE Study Bible Name List nor BDB Theological Dictionary care to interpret this name.