Both 'Becker' and 'Barber' are names with Jewish origins. I could find no records on the name 'Schwerzmann'.
This name seems to have originated in the late thirteenth century and as you might expect, means someone who cut hair for a living. As with many occupational surnames, the name cuts across many ethnic groups, as most people need their hair cut, regardless of religion! The word barber comes to us from the French word for beard ('Barba') and spread across into Germany, Denmark (and their respective Jewish communities) and other parts of Europe when surnames began to be customary.
This name has similar roots but goes back even further and with a few extra deviations. Although a variant on 'baker', this doesn't just mean anyone who made bread for a living, but anyone who baked using an oven - including people who made bricks. The word comes from German, with 'bach', meaning stream - perhaps to do with the mills required to make flour. The name spread for the same reasons as with 'Barber', with tax laws required specific names to be allocated to each person.
The history of Jewish names is an interesting one, as we see from this recorded lecture: