System Information
Windows 7 64-bit, Nvidia gtx570

Blender Version
Broken: official 2.7 and 2c00ecc (latest 64-bit build)

Short description of error

I'm not quite sure which part of this is the issue and which are intended features:

Choosing Object> Make Links> Object Data will link a vertex group to another object (if the target object already has a vertex group). Although the vertex group will be linked, so editing the vertex group on one object will change the group on the other, the existing vertex group name will not have been changed. Editing the name of either vertex group will not effect the link between them.

If no vertex group is on the target object when linking, then no vertex group is copied/linked to target object.

Adding a new vertex group to either object does not add the vertex group to the object with linked data so I'm not sure if vertex groups are only meant to be copied during linking operation, but then why are changes updated between groups? Or they're meant to be linked but the name doesn't change and new groups aren't linked.

Exact steps for others to reproduce the error
Based on a (as simple as possible) attached .blend file with minimum amount of steps

Using attached file (objects have mask modifiers to visualise vertex groups):

1. Select target object, Plane 2
2. Shift select original object, Plane 1
3. Ctrl + L, choose 'Object Data'
4. Plane 2 has Plane 1's vertex group but name of vertex group on Plane 2 is unchanged.
5. Enter edit mode of Plane 2 and remove a vertex from the group, exit edit mode to see Plane 1 also update changes.
6. Add a new vertex group to either object to see that it isn't added to object with linked object data.