There isn't a single, universally recognized nickname for the Paleozoic Era. However, some common terms used to refer to it include:

* "Age of Invertebrates": This is a popular nickname because invertebrates were the dominant life forms during this era.

* "Age of Fish": While invertebrates were abundant, the Paleozoic Era also saw the rise and diversification of fish.

* "Age of Trilobites": Trilobites were a highly successful group of marine arthropods that thrived during the Paleozoic Era and are often used as a symbol of the era.

It's important to remember that these are just nicknames and don't fully capture the vast diversity of life that existed during the Paleozoic Era.