Defining a type of matrices I was wondering if there is a name for matrix like following:

It is like a symmetric matrix but to the other side. Is there a definition for this type of matrices?
 A: As @user1551 mentioned, this is a Toeplitz matrix:
https://en.m.wikipedia.org/wiki/Toeplitz_matrix
A: Disclaimer : I stick to your definition "It is like a symmetric matrix but to the other side". I don't take into account the supplementary fact that all descending diagonals contain the same entry that exists on your example but may not exist as well.
Up to my knowledge, this kind of matrix has no special name. Let us call them provisionally $T$-matrices.
It must be understood that all operations that can be done on $T$-matrices are literally "mirrored" into operations done on symmetric matrices $S$ through operation ;
$$T \to JTJ=JTJ^{-1}=S\tag{1}$$
with matrix $J$ defined by :
$$J:=\begin{pmatrix}0&0&0&1\\ 0&0&1&0\\ 0&1&0&0\\ 1&0&0&0\end{pmatrix} \ \ \ \text{with} \ \  J^2=I \ \iff \ J^{-1}=J$$ 
(or the equivalent in $n$ dimensions). 
Remark : (1) is a bijection, with inverse operation $T=JSJ$. Moreover, this relationship shows that $S$ and $T$ are conjugated ; thus in particular, they have the same eigenvalues.
