I'm asking if there is anyway in blender to make more than vertex groups assigned to only one bone? lets say I have a only one bone in cube and I want to assign four different groups representing the four corners of the cube. If anyone could please advise how to do that as from what I know that to link vertex groups with bones the names needs to be the same, but in my case there will be only one bone name and four different vertex groups names, so then how I'm gonna link those four vertex groups with this one bone if they have different names?
You can not assign more than one Vertex Group to one Bone. However you can assign many vertices to a vertex group where each vertex may have different weight. And that should be exactly the solution for which you are searching.
There is no benefit from splitting the weights for one single bone into different vertex groups. Even if that would be possible, blender had to merge the groups anyways before it could apply the weights to the vertices.
Please also check the wiki documentation about vertex groups:
You should read all 4 chapters of that section.