I have an i-VTEC engine, which Honda claims to be a better and computerized version of their famous VTEC Engine.
Now I am wondering: Is it right to tell people that only HONDA has VTEC? or is this technology distributed to other manufacturers as a different name?
Honda VTEC is famous for their VTEC's "Kick in power", are there similar existing technologies that are originally from other manufacturers?
The Wikipedia article on VTEC should be good at helping you understand it all. VTEC is a trademark of Honda's patented technology (the original patents have expired but Honda have patented newer implementations such as A-VTEC). So no other manufacturer's production engine can do exactly the same thing. However, that doesn't mean they can't be similar.
This explains Honda's VTEC and Nissan's Neo VVL which both use switching/changing cam technology.
There are many other methods of variable valve timing, but I couldn't find any other modern production methods like VTEC.
So yes, VTEC is Honda only and yes, there are other technologies that achieve the same, or very similar, goals.
While not necessary, I found this video to be very intriguing and good at explaining the basic workings of V-TEC.
Here's a little something to read as well which compares VTEC to Toyota's VVT-I method.
VTEC is what Honda are calling their implementation of variable valve timing. Each manufacturer has their own version of it, each with their own name. See here for a list.
So, you are right in saying only Honda's have VTEC. But other makes have a system doing essentially the same thing, they just call it something else.
The last line of your question "Are there existing technologies that are originally from other manufacturers?" depends on your definition of VTEC.
VTEC gives you the "kick" as the camshaft profile changes. To understand the reason for this, you have to look at the difference between high performance race engines and those used in road cars.
Typically a fully race tuned engine will be lumpy and gutless in the lower RPM band. It will have an erratic idle and will be easy to stall. This is because it will have a race camshaft which opens the inlet valves very early, it may hold the inlet and exhuast valves open at the same time to improve chamber filling using the negative pressure in the exhaust (i.e. scavange it's inlet plenum) and it will keep the valves open for as long as possible to let the maximum about of air/fuel mixture into the cylinders. This makes for an engine which produces significant amounts of power when revved hard, a "screamer".
However, as a road car, it doesn't work. When you're nan is popping down to the church on a Sunday, she doesn't want to have to bounce the car off the rev limited and nearly spin the wheels everytime she pulls away from a stop. Race cars also use massive amounts of fuel, indeed the Viper does about 4MPG at full race speed. In road cars, relatively mild cams are used which allow for smooth running and plenty of low down torque so that it's easy to pull away from near idle at a very small throttle opening without stalling.
Variable Valve Timing is not a new concept. It is a way that combines the best of both worlds so when you're bumbling around a car park looking for a space, your car is smooth and not using massive amounts of fuel but when you need some power to overtake a truck, the car behaves as though it has a full race camshaft and gives you a significant hike in power. This is done by having valves that do not open for a fixed duration across the rev range and in all conditions.
If you look at the large static steam engines of the 1850's, you'll find the use of Rotary Valves in the likes of Corliss engines. The patent for these goes back to 1849.
In the automotive world, Porsche made a patent application in 1959 for an Oscillating Camshaft system that would dynamically adjust lift and duration in differing engine conditions.
As regards actual automotive implementations, numerous manufacturers have their own systems and brand names for variable valve timing which work in different ways. For example, Alfa Romeo introduced a commercial cam variator on the 1987 Alfa 75 Twinspark. Volkswagen employed a similar setup using hydraulics within the actual camshaft drive gear on their VR6 engines.
Fiat have recently (commercially available in 2009) developed the Multi-air system which using electronically controlled hydraulic actuators so that they can adjust valve duration on a stoke by stroke basis. This represents absolute control as it negates the need to select any fixed camshaft profiles or starting cam positions.
The Porsche system eventually became VarioCam and was used on the 968. The effect of this and many other systems is far more subtle than VTEC because these systems dynamically alter the cam profile whereas VTEC, in it's most basic form, employs two camshaft profiles and there is a noticeable "kick" when it activates. That said, I can personally say that BMWs VANOS system does a similar thing and it's definitely noticeable when it activates although it isn't quite as sudden or pronounced as VTEC.
VTEC is of course the protected brand name of a system used by Honda so any other manufacturers wishing to say their car had VTEC would have to pay a royalty to Honda or risk being sued out of existence. This does not mean however that it was Honda who came up with the concept that adjusting lift, duration or cam timing as the requirements on the engine change. The concept and alternative implementations exist at least as far back as 1849.
