Our cows have had names and now have numbers and I can't say as it really has made a difference. I was the cow namer and when I quit doing barn chores that kind of went by the wayside. Our cows have listened to rock, metal, NPR and country and they don't really seem to have much of a preference. Personally, I think they were fans of what is now called easy listening (60s and 70s pop, the British invasion etc.) I do know there was one cow who did not like metal, but she seemed to be alone in that particular preference.
Ah, Elsie and milk from contented cows. What it really comes down to is how you treat your animals, feed them, give them enough space and water and their innate abilities to produce milk and their personalities. Brainless as they are, they do indeed have distinct personalities, and different production potential.