Is gravitational wave a new category of wave? We know that there are 3 kinds of waves.
Mechanical wave,
Electromagnetic wave,
Matter Wave.
Since the theory of gravitational wave is confirmed, will it be called a new type of wave? Will it be enlisted in the list above? If it does why and if it doesn't, why not?
I do not like your characterization of the type of waves.
In physics there are three main types of wave equations, i.e. equations whose simplest solutions are sinusoidals, fitted to observations.
a)Waves on a matterial medium, as water waves, sound waves, the energy is riding on the material in a sinusoidal manner.
b)Waves where sinusoidal solutions in space time are fitted to fields carrying energy, where there may be no material medium. These are the electromagnetic waves in spacetime and gravitational waves in spacetime. Electromagnetic waves and gravitational waves can propagate in a medium, but what separates them from matterial waves is that they also propagate energy in empty space.
c)Probability distributions , from solutions of quantum mechanical wave equations, as the Dirac and Klein Gordon. These are sometimes mistakenly called "matter waves", which can show sinusoidal distributions.
Since the theory of gravitational wave is confirmed, will it be called a new type of wave? Will it be enlisted in the list above? If it does why and if it doesn't, why not?
Yes, the discovery confirms a separate type of energy transfer through gravitational waves, which had been predicted by Einstein from the General Relativity equations, and they are a different wave than electromagnetic waves which are predicted by Maxwell's equations.
Categorizing objects is often a useless platonic pursuit, and categorizing waves fits into that category. Ha. When you try to fit waves into different boxes you lose sight of what a wave really is. Rather than looking at the differences look at what's common, what's fundamental.
In the most simple manner, waves are just an expression of the flow of energy through time and space.
Waves are the changes we observe in matter and fields that tell us energy is flowing.
Formally, any smooth function can be represented as a sum of sinusoidal waves; which isn't helpful in categorising waves.
Before Einstein, light was theorised as a mechanical wave in a matter-like medium, the luminiferous ether; now it's considered as a wave whose medium is spacetime itself.
This suggests that categorising waves by the medium it moves in is useful in physical descriptions.
Given this, then the answer to your headline question would be yes; since such waves have been theorised, but not observed; and now they have been observed - importantly, since physics is an empirical science.
