Essex comes from Old English Eastseaxan, literally "East Saxons". In other words, this is the part of England that was invaded/settled by the Saxons and they divided their lands into east, south and west regions, plus a middle region (middle Saxons, modern-day Middlesex).

There's no Norsex because at that time the lands to north of Saxon territory were held by the Angles. They also divided themselves into East Angles, South Angles, etc., but those names don't seem to have survived into the modern day. Interestingly though, the Kingdom of East Anglia was divided into "North Folk" and "South Folk", which is the origin of the modern-day names for Norfolk and Suffolk.

If you've heard of the Anglo-Saxons, yeah, that's these guys, the Angles and the Saxons. The Angles came from parts of modern-day Denmark, the Saxons from parts of modern-day northern Germany. They shared a lot of common Germanic culture but were also rivals.