I was watching passion of Christ and there's a scene when Jesus is whipped very badly before being crucified. I was wondering what you'd call one of those big brawny guys with the whip. Maybe punishers? Whippers? They can't be executioners can they?
It depends on the situation
a resident executioner would also administer non-lethal physical punishments, or apply torture.
This seems to be more of a full time job, where the local, well-trained executioner (who carried out a death sentence) would also carry out other punishments, possibly such as whipping or flogging.
An inquisitor was an official (usually with judicial or investigative functions) in an Inquisition
The inquisitor was more of an administrator in the room, while the people carrying out the actual torture may have been anyone operating under the inquisitor.
These articles refer to the people who carried out the punishment as a "torturer":
The Roman officials who carried out floggings were known as Lictors.
Lictor, plural lictors or lictores, member of an ancient Roman class of magisterial attendants, probably Etruscan in origin and dating in Rome from the regal period. Lictors carried the fasces for their magistrate and were constantly in his attendance in public; they cleared his way in crowds and summoned and punished offenders for him.
A few whipping-specific words come to mind: flogger, scourger, and flagellator, all nouns formed from verbs.
1. FLOG, WHIP
2a. :to punish severely
1a. : to beat with or as if with a rod or whip
1. : WHIP, SCOURGE
2 : to drive or punish as if by whipping
Definitions from Merriam-Webster Online
All have the additional benefit of being (ultimately) derived from Latin, the language of the Roman soldiers who did the scourging in that film.