Many programs on internet and TV try to attract customers by teaching through games,so what is the name of this combination?
I often see the word "Infotainment" used in in this context, which is a portmanteau of Information and Entertainment.
Another word that comes to me is "Gamification" which can be defined as converting something to a game in order to trigger the desired behaviour. This very site is an example of that.
(Wikipedia links added for additional reference)
The term Edutainment was used for a while, but I don't think it caught on.