I have about half of them named, I don't have a system, I just name them something appropriate for their looks and personality:
Our top Delaware Rooster is named Roaster;
His girls are Hanna and Pixie (BO) and Henrietta and Zelda (RSL)
Our GLW Roo is Sylvester (formerly Sylvia) he was supposed to be a pullet, and his girl, Goldie.
The triplets (RSL) Eloise, Madeline and Cleo (all named after children's book characters);
A Black Australorp named Beauty;
Our 6 Barred Rock/?? mixes, the Roos are Splash and Rocky (his duck and weave is legendary) and the girls Roxanne (all the boys love her), Lucy and Ethel (I Love Lucy, they are BFF), and Jewel (daugher picked name, I don't know why)
We have a bunch of meat bird that are just referred to as "meat"
And 10 5 week old mixed breeds that came with Beauty that have yet to get names. The boys will be meat, the girls will be named. I think one will be called Sasha.
I have to talk to them and call them by name every day or else I'll forget their names.
I do like the idea of naming them after greek gods and goddesses, so the new ones might all fall into that naming trend.