I deliberately got different breeds because I was positive I wouldn't be able to tell them apart otherwise. (Never had chickens before I dove into this Chicken Thing last October.) Imagined if I had a flock of six RIRs, it would be like, "Good morning, Rhoda. 'Morning, Rhoda. How are you, Rhoda? Good morning, Rhoda. And you too, Rhoda. Oh, mustn't forget you, Rhoda, good morning!" So I bought all different breeds.
However, when I bought two Golden Lakenvelders from another BYC member, I did see the difference between them and now can say, "Good morning, Millicent! How are you, Minerva?!"
And as to whether they know their names or not... well, Carl the rooster does, and Betsy the BR does, and so does Matilda the BA and Ellen the bantam lavender Cochin. The rest of them, not so much. Not even Rhoda the RIR, but she's still young.
EVERYBODY comes when I make my chicken call, "Chickens! I have CHICKENS!"