Can my employer force me to give my full name to the client?

I worked in quality control department for the past 3 years and we always used little stamps with a single number on it (eg mine was 5 and meant work station no 5). About 5 months ego our management decided we should be writing our names on each box we inspect and recently they gave as special stamps with our names on it. My friend who is African and some eastern european staff think that they are receiving more complaints than before because their names sound foreign and we all start to wonder if we can do anything about this new policy. Any ideas?