You can iterate over the components of the dimension block definition to obtain the MText entity which displays the dimension text - refer to my LM:getdimstring function as used in this post for an example.
Have you considered just getting the name of the acad object?
(setq acadObjName (vla-get-name (vlax-get-acad-object)))
For reg autocad it should be "Autocad" and for civil 3d it should be "Autocad Civil 3D (year)"
At least for me it is.