At the moment HUD attachments will only display the owner name when you point the mouse cursor at them (as tooltip text / hovering text). When rezzed on the floor instead of being attached, they display a different tooltip text (object name, owner name, script type).
That shows the client already makes a distinction here and displays a different text when the object is worn. Would it be possible to add a LSL command like llSetTooltiptext? It would make sense to name HUD buttons that only show images, instead of trying to squeeze the text into the textures. It could work similar to llSetText.