pooch · noun1
Of uncertain origin. One (unsubstantiated) conjecture is that the word comes from Putzi, a common German name given to lapdogs. The name Putzi is possibly formed from German Putz + -i, influenced by German putzig (“funny, cute, small”, adjective).
pooch · noun, verb2
Probably related to pouch.
Etymology from Wiktionary, CC BY-SA 4.0.