My question is apart from the C in the straight chain with $\ce{-OH}$ group, should $\ce{N}$ be counted as chiral center since it also has tetrahedral geometry and all different substituents?
There are more such examples.
My question is apart from the C in the straight chain with $\ce{-OH}$ group, should $\ce{N}$ be counted as chiral center since it also has tetrahedral geometry and all different substituents?
There are more such examples.
You can surely count that nitrogen atom as a "chiral center" because it has four different groups attached to it.
However, the net optical activity due to that chiral center is zero because the two optical isomers from that nitrogen atom are rapidly interconverting with each other ("Amine inversion"). They always exist as a racemic mixture, and hence are optically inactive.