You can make coconut milk as creamy or as thin as you desire (think homogenized milk vs. skim). It’s all whatever tastes good to you!
Reason’s why your milk may separate:
Using a regular blender. Because it cannot reach the speed of a Vitamix style blender, your milk may not be able to stay in emulsion.
Also water temperature will also play a part in its separation – too cold and it will separate. However, separated coconut milk does not affect the taste, and can easily be mixed back up by shaking it before using.