I'll be honest, apart from their logo on Bethesda games I know nothing about them.
When Bethesda started buying up other companies the internal studio wanted to differentiate between
Bethesda games (Elder Scrolls, Fallout) and their published titles (which would later include owned stuff like Dishonored and Doom but at the time included stuff like the masterpiece Rogue Warrior, the Pirates of the Caribbean license, Wet, the Star Trek license, etc.) in a clearer way. ZeniMax was already the legal name of the overall holding company they just never used it beyond that.