The 501st began the inspiration for the nickname "Vader's Fist" when they raided the Jedi Temple with Darth Vader, executing every single Jedi they could find after Order 66 had been issued. Some of them tussled with Yoda and Obi-Wan Kenobi later on, and didn't live to tell about it.
The 501st had many commanding officers in their time.
Some of their Clone Commanders:
The 501st had blue markings, which they altered just before their raid on the Temple. They knew they were following Anakin Skywalker, so they painted big blue "A"s on their chests. They were a little embarassed when they found out he'd changed his name to Darth Vader, and claimed it was actually just a lower case "i" with a triangle over it instead. Vader saw through their deception.