It is important to uniquely name data frames because data frames get identified by using their name. Therefore always use unique names for data frames. If a data frame is not named uniquely within an ArcMap document (mxd file) then it is not possible to uniquely identify ArcGIS Server resources like data frames or layers anymore.
Unique data frame names are the prerequisite for providing proper and correct
•Printing (especially for printing map collections, i.e. multiple blended maps),
•Layer specific functionality like querying, selection, editing
•Etc.

Unique names for dataframes
It is possible to work with data frames named identically when using different mxd files (See How can I use caches although my users want to switch layer visibilities?). To identify a layer, WebOffice 10 R3 needs a unique combination of map service, data frame, group layer and layer.