Guess most things that start with 'cyn' are doggie, but it hadn't ever crossed my mind before as I'd never have described the lovely dog as cynical!
But Wikipedia comes up with the rationale behind it:
The name Cynic derives from the Greek word κυνικός, kynikos, "dog-like" and that from κύων, kyôn, "dog" (genitive: kynos). One explanation offered in ancient times for why the Cynics were called dogs was because the first Cynic, Antisthenes, taught in the Cynosarges gymnasium at Athens. The word Cynosarges means the place of the white dog. It seems certain, however, that the word dog was also thrown at the first Cynics as an insult for their shameless rejection of conventional manners, and their decision to live on the streets. Diogenes, in particular, was referred to as the Dog, a distinction he seems to have revelled in, stating that "other dogs bite their enemies, I bite my friends to save them." Later Cynics also sought to turn the word to their advantage, as a later commentator explained:
There are four reasons why the Cynics are so named. First because of the indifference of their way of life, for they make a cult of indifference and, like dogs, eat and make love in public, go barefoot, and sleep in tubs and at crossroads. The second reason is that the dog is a shameless animal, and they make a cult of shamelessness, not as being beneath modesty, but as superior to it. The third reason is that the dog is a good guard, and they guard the tenets of their philosophy. The fourth reason is that the dog is a discriminating animal which can distinguish between its friends and enemies. So do they recognize as friends those who are suited to philosophy, and receive them kindly, while those unfitted they drive away, like dogs, by barking at them.