You could use a docked cell with the version number in it. Here's a starting point:
SetOptions[$FrontEndSession, DockedCells -> Cell[BoxData[ ToBoxes[NumberForm[$VersionNumber, ], StandardForm]], "DockedCells", ShowStringCharacters -> False ]]
(Note that $FrontEndSession
won't persist past quitting the front-end.)
Edit
Here's a version with an orange background that goes edge-to-edge. The key option is CellMargins
:
SetOptions[$FrontEndSession, DockedCells -> Cell[BoxData[ ToBoxes[NumberForm[$VersionNumber, ], StandardForm]], "DockedCells", ShowStringCharacters -> False, CellMargins -> {, }, Background -> Orange]]