Symmetry C3V For MeCl
You've correctly identified the $C_3$ axis that contains the $\ce{C-Cl}$ bond.  Methyl chloride also has 3 planes of symmetry that contain the $C_3$ axis and each of the $\ce{C-H}$ bonds.  Since these planes contain the $C_3$ axis they are referred to as $\sigma_{v}$ planes of symmetry.  There are no other symmetry elements in methyl chloride so it belongs to point group $C_{3v}$ (n $\sigma v$ planes plus a $C_n$ axis).  

There is no $C_{nd}$ point group.  There is a $D_{nd}$ point group which contains a $C_n$ axis, n $\sigma_{v}$ planes (so far methyl chloride fits the description), but also n $C_2$ axis.  Methyl chloride does not contain any $C_2$ axes, so it does not belong to the $D_{nd}$ point group.