This is one of the little tidbits I've integrated into my own mod, although it was really an incidental part of a much larger change (overhauling the Unit Panel to use two rows of promotions instead of just one, but shrink a bit horizontally to keep from taking too much real estate). It's an incredibly easy thing to add, but it requires altering one of the game's UI Lua/XML file pairs (in this case, UnitPanel), which makes that sort of mod incompatible with any other mod altering the same bit of UI.
Alternately, you can just open FireTuner and rename the unit by hand with a Lua command. This assumes you've enabled the Tuner and know basic Lua commands, of course.