What carrer I should study to be a videogame designer?

As someone who is a heavy gamer, I have done a fair amount of research on this. Put simply, find out what specific area of video game designing you would prefer to work as.
Game Tester
Graphics Designer
Content Writer
Game Programmer
etc.

Each one of these fields require a different set of skills and a different degree would help you start your career in the correlating field. I would recommend going to the LinkedIn page or website of your top favorite video game producers and read some of the available positions they are looking to fill. They will describe what the role entails and if you are interested, you can read up on the skills required to fill the position at the company. You can then strive to build those specific skills.

Which career should you study to be a video game designer, there are many different areas to be a game designer. Here's what I think are the keys areas to every game: 2D/3D Designer, Game Tester, Game Programmer, and Video Game Writer.

2D/3D Designer are the ones who create the models of the character in 2D or 3D.

Game Testers are the ones who tests game and give feedback and may learn how these functions work in the game which could lead you to upper jobs in each company.

Game Programmers are the ones who write the codes and functions of the game, levels, and characters.

Video Game Writers are the ones who writes the plots, dialogues, the character creations, and developments of the video game.

Depending where you live and what you want to learn, you can go from there. I would just dive into one of the game engine programs to get the feel.

Unity 3D is the highest quality game creation engine I have used. And, you can learn how to use the program in definite by learning through the tutorials on Unity.

Seems like this is a popular topic. :)

Let me first start by saying I am not (and have not been) a video game designer. I have been in Software Engineering for 30+ years now, and have seen the game industry grow and change (along with the software industry as a whole). The advice so far has not been bad, but let me try to add some perspective.

Watching the credits on a feature film (or on a video game) shows you the hundreds of people involved in video game production. Not all of those jobs are glamorous or fast paced... a lot can even be considered WORK. :) But it shows the range of talents that are needed in these fields make a game or film today.

Oddly enough, these are the same skills needed for a lot of other fields. I work in telecommunications, and the need for people to store our software, document what it does, test it works correctly (not to mention actually writing the code!) involves a lot of the same skill sets that people use in the gaming field... or the medical software field... or financial software... or a host of others.

A degree involving software will teach about how to do SOFTWARE, and that is pretty much independent of the domain where it is used. Yes, you do need to learn about domains like gaming, or telecom, or medicine, or finances to be effective in each domain. And liking the field of application is nice. But "sorting data is sorting data" regardless if is in a bank.. or in a game.

If this field fits your interest (and it may or may not... a lot of people start a software degree and don't finish) I think you will find opportunities in and beyond the gaming domain. You might be surprised that a good "configuration manager" (which you may or may not have heard of) may be more in demand at a gaming company than a coder. A good degree at any level in software allows you opportunities in a lot of fields... gaming included. :)

Keep exploring! Learn more about what programs are possible for you, and which are best regarded. Best of luck!