Caller name instead of number

Hello, first of all I am glad that I found this place, seems very helpful.
I am a supervisor at a call center and I am facing a big issue-we manage to speak to only 20-22% of the customers we call. The others don’t pick up regardless how many times we try to call them. The phone numbers are valid (or at least not more than 10-15% are fake), customers are from European countries. We call from 9-10 AM UK Time until around 20:00 PM. We are using a predictive dialer, but calling manually doesn’t change the situation. For me it is strange that we reach so small part of our customers, however my manager says it has always been like this, so “it is ok”. I want to prove that we can do better. Have you faced the same problem, how did you manage to improve your statistics?
When we call, customers see a strange UK number, maybe they don’t pick up, because they think it is a scam and they will be charged money? I know that it is possible to show an agents name instead of a number, but don`t know if it depends on the software or our voip provider maybe. Any suggestions?
What are your statistics, have you faced the same problems?
Thank you all.