We would actually have to see your code to answer this question, for your ESP Names, make sure you're assigning the player's name to each player correctly.
Also when you saidI don't quite understand what you said there, do you mean your esp only works for about 20 seconds then shuts off? Is it for your entire ESP or just 1 feature. Make sure you don't have any type of timers enabed when turning on the ESP.... esp stuff works for like 20 seconds then does nothing and then works again ?