Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
If the alcohol-free beer you mentioned in your question does not intoxicate (cause drunkenness) then it is lawful to drink it.
Calling it beer does not influence the rule as such a drink is originally lawful. Indeed, the rule depends on the reality of the thing on its label.
But anyone who wants to drink this should make sure that what he drinks is the brand that is alcohol-free, not the other one that looks like it but contains alcohol.
You may also want to consider that many of these products are made by beer-producing companies and when you purchase the non-alcoholic drink you are still supporting the alcohol producers.
Allah knows best.