The CEO, Evan Greenberg, is the son of former AIG CEO Hank Greenberg. Unlike his dad, the guy’s a Democrat.
https://www.campaignmoney.com/political/contributions/evan-greenberg.asp?cycle=16
Evan Greenberg was a great admirer of Michael Bloomberg. Evan Greenberg was the CEO of ACE Insurance, and ACE — which was a big player in commercial insurance — acquired Chubb, a multi-line insurer, which was well known for writing upscale personal insurance. Since the Chubb name was well known, and that name was in itself a great marketing tool, the new merged company dropped the ACE name and kept the Chubb name.