how do you call this job in English?

What do you mean by "stores"? In English, a "store" is a place that sells goods, a shop. It can also mean a quantity or supply of something kept for use as needed, supplies. (usually "stores").

Someone who builds or repairs windows would be a "window installer." The person who fits the glass into the window is a "glazier." I found a number of businesses that describe themselves as "window specialists."

I am not sure I have a name for someone who installs screens and shutters. By searching, I found things like "window screen repair technician."

Another name that might be used for someone who fixes things on windows & doors is "handyman." This person does not specialize in windows, though. It's " a person (especially a man) who is skillful at doing small jobs (such as household repairs)" You hire a handyman to replace the window screens, mend the fence, fix the hole in the wall, install shelves, and much more. "Handyperson" which sounds a bit awkward, is the gender-neutral version.

Ah! Found it! Stores are window blinds, also just called "blinds." There is a standard joke: A sign on a truck

I'd probably just call the person a "shutter installer/repair person" or a "blind installer/repair person."

Informally, I'd probably say something like "the shutter guys will be here at 11."

In N.Z and Australia, there is no specific name. Shutter Repairer or Shutter Installer, would be typical. For glass windows the word Glazier is common.

It sounds like the products you're talking about are the roller type security doors/screens, sometimes called "roller doors".

Other terms might be window security, door security, locks, roller shutters, concertina grilles, burglar bars, steel security doors, anti-vandal screens and security cages.

People who install such doors are called "fitters" or simply installers. Possibly, there are other terms in other countries?

In the US, we wouldn't use "fitter." We'd say "installer" or maybe "technician," depending on the situation.

The only "fitters" I know of are ladies who measure other ladies for brassieres.

Fitter is a common term in the English (i.e. non-US American English) language. Without knowing the origin of the OP, fitter is the best and most widely used English language word. You did see that I also included the term "installer"?

Yes. My comment was meant to simply note that "fitter" is not American English.

This reminds me of the very amateurish sign I saw in Israel, clearly translated by someone who thought he didn't need to request the assistance of a native English speaker:

"....bathtubs, floor tiles (whatever....), shatters windows..."

'Store' is french. Used for awnings as well as blinds.