Without ever thinking hard about it I always assumed git came from American cowboy/western slang:

Specifically this: https://en.wikipedia.org/wiki/Git_Along,_Little_Dogies

Every time I type it in I am visualizing my little code changes as sickly orphaned calves being herded into the main pen with all the mature cows currently working away at their various functions.

Of course given the actual author the British/European meaning makes a lot more sense.