I was wondering whether BEATUS was used in the Roman world before there were Christians. If so, I suspect it was the expression of the parents' wish that their child should be happy. Maybe it was just the translation of the (old) Greek name MAKARIOS?
If the name did not exist before Christian times - does this mean it came up because of Jesus' Beatitudes? Could it have been designed to anticipate the possible fate of a Christian child in a non-Christian world: to suffer persecution? C.f. Matthew 5:10-12.
Or if it did exist - did maybe Christians reinterpret the name in this way?