Can that be changed? Is it just convention? Is there any commercial bike that comes with a left-shifter that switches cogs?
I would not call it convention but rather a reasoned design choice: most people are right-handed and one shifts the rear gears more frequently, therefore right shifts rear. This is the same worldwide for all integrated shifters, which integrate the brake and shift mechanics.
Brakes however are often reversed in countries, like the UK, where traffic runs on the left side of the road. This is indeed a convention and can be easily changed.
It is not possible to swap the gear shifters, using off the shelf components, without making some changes, e.g. the cable routing under the bottom bracket. Therefore, I would abandon this idea except if there is some medical reason, which makes a change necessary.