These personal protectors will be able to take many shapes. Robotic or manned. Integrated or separate.
Most likely, such a company will begin by creating small groups of drones that can be rented by ships.
These drones would act as scouts generally, but could be used as killer satellites, ramming other ships, should a ship ever be attacked. By the time such devices are needed AI will have developed enough that remote control will not be necessary. The protectors will be able to behave as a dog would when its owner says "sick'em."
As time goes on manned craft will be developed that will essentially be escort fighters. This would be a very elite type of group probably only contracted by dignitaries or large corporations.
The need for protection of standard cargo and transport ships will decrease as more are launched and used. Therefore, such a security force will quickly become something for the niche market of the very paranoid or the very rich and important, just as private body guards today.
The primary reason that such force will be needed more in the beginning is because the harshness and greed in space will create the same kind of desperate crime that existed during the California Gold Rush. Those in space will need a body guard or guard dog just as the western prospectors once did to protect their claims and supplies.
Certainly, these types of "body guards," manned or unmanned, would require changes to current space law, that prohibit such weapons in space, in order to exist. But such changes will come about when those in space need protected as much as the people on the surface of a planet.