Quoting from wikipedia:
Canis Minor was one of the original 48 constellations formulated by Ptolemy in his second-century Almagest, in which it was defined as a specific pattern (asterism) of stars; Ptolemy identified only two stars and hence no depiction was possible. The Ancient Greeks called the constellation προκυων/Procyon, "coming before the dog", transliterated into Latin as Antecanis, Praecanis, or variations thereof, by Cicero and others. Roman writers also appended the descriptors parvus, minor or minusculus ("small" or "lesser", for its faintness), septentrionalis ("northerly", for its position in relation to Canis Major), primus (rising "first") or sinister (rising to the "left") to its name Canis.
It looks like the original (Greek) identification of the constellation by Ptolemy didn't attribute anything to it, let alone a dog. But over time, the constellation became known based on its proximity to Canis Major. Originally known as Procyon meaning "coming before the dog", i.e., it rises before Canis Major. This relation to Canis Major seems to have led it to being considered as a representation of a dog as well. The Minor attribute appears to be due to the fact that it is fainter overall than Canis Major.
Really though, you can't pick apart constellation patterns too much. Much of them don't look that much like their attributions and only evolved over thousands of years of stories and imagination. It's not like one guy sat down one day and said, what does this pattern of stars remind me of, and that was that.