How to say in English (is there single word) for selling program: you buy an item and then you can have some discount on next one (the same or of another kind)?
The single word you may be looking for might either be sale or promotion.
When a product is on sale it is usually sold at a discounted price to the regular price.
When a product has a promotion it will usually have offers of multiple buys at a discounted price or some connection with other products in the same promotion.
In BrE when a product is on sale or being promoted it is referred to as begin on offer.
As has been mentioned in the comments, usually the name of the sale is a shortened form of the terms of the promotion, like "Buy one, get one" or "Buy one, get one half off". Sometimes "Buy one, get one" is referred to as a BOGO sale and "Buy one, get one half off" is BOGOHO because they are both well-known types of promotions.
Another example is a "one cent sale" where if you meet some requirements, you may buy something for a penny. There are additional terms, for example, not everything in the store is eligible to be bought with a penny, but most people understand that even thought the description doesn't explain that.