According to Targum Yonason Ben Uziel, (31:8), Bilam was notorious for 4 attempts to destroy the Jewish people. The name Bilam hints at these four attempts.
1) He was Lavan HaArami, who wanted to destroy our forefather Yaakov.
2) He advised Pharaoh to torture the Jews in Mitzrayim.
3) He incited Amalek to declare war against the Jews.
4) Upon Balak's invitation, he came to curse the Jews, and he advised Balak to encourage Z'nus among the Jews.
The word Bilaam (Bes, Lamed, Ayin, Mem) is an acronym for Balak, Lavan, Amalek, and Mitzrayim.