Lets imagine that I have a simple sinusoidal wave form like this
It is possible, to by design ended up. Like this :
So that ended up having a new/different sound timbre? If it is possible, how this concept is called?
Yes of course many synthesizers let you design your curves. You can call it curve design, curve drawing, curve morphing, wavetable design and many others along these lines. You can get pretty elaborate with it and achieve nearly whatever design you have in your head (for example start with this "skewed" sine wave and then end up in a pure sine, no limit whatsoever.
A good example of a synth that can go very deep into this kind of stuff is Zebralette by U-He. It's a free synth that lets you manipulate the waveform in all sorts of ways. You might have to do some searches and try some VSTs to end up with the one you like but this is something doable.