If you omit this labelling, it makes little difference. But if you invent your own, different, system of labelling, it will cause trouble when you play against another program which uses the conventional system. This is far more confusing than just omitting the labels. This should be easy to do, even with an ascii-art board. It makes it easier to see where your program has played.
Human beings make mistakes.
When the person operating your program inputs its opponent's move, he will get it wrong at least once per game, and need to undo it. If it is not possible to undo the last move, you may find that you have to forfeit the game. Indicate when you have moved When your program moves, it should make it clear that it has done so. An effective way to do this is by an audible beep. Remember that the program's operator may have his back turned to the screen so that he can talk to someone.