A dictionary of Proverbs (Oxford Paperback Reference)

Give a DOG a bad name and hang him
The principle is that a person’s plight is hopeless once his reputation has been blackened. Similar to he that has an ILL name is half hanged.

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  1706 J. STEVENS Spanish & English Dict. s.v. Perro, We say, Give a Dog an ill name and his work is done. 1721 J. KELLY Scottish Proverbs 124 Give a Dog an ill
  

Name, and he’ll soon be hanged. Spoken of those who raise an ill Name on a Man on purpose to prevent his Advancement. 1803 Norfolk (Virginia) Herald 14 Apr. 3 It is an old saying, ‘give a dog a bad name and hang him’. 1928 G. B. SHAW Intelligent Woman’s Guide to Socialism lvii. The Liberal impulse is almost always to give a dog a bad name and hang him: that is, to denounce the menaced proprietors as enemies of mankind, and ruin them in a transport of virtuous indignation. 2002 Times: Weekend 20 July 4 Give a dog a bad name seems to have become a workaday motto for the wine trade. And the sillier the name on the bottle, the less chance there is of anything drinkable inside. ■ reputation; slander
DOG does not eat dog
Cf. VARRO De Lingua Latina VII. 32 canis caninam non est, a dog does not eat dog’s flesh.

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  1543 W. TURNER Hunting of Romish Fox A2^V The prouerb.. on dog will not eat of an other dogges fleshe. 1790 ‘P. PINDAR’ Epistle to Bruce 31 Dog should not prey on dog, the proverb says: Allow then brother-trav’lers crumbs of praise. 1866 C. KINGSLEY Hereward the Wake II. xi. Dog does not eat dog and it is hard to be robbed by an Englishman, after being robbed a dozen times by the French. 1933 F. D. GRIERSON Empty House viii. Dog doesn’t eat dog, my dear fellow. To put it more politely, the physician attends his brother practitioner without charge. 1993 ‘c. AIRD’ Going Concern (1994) viii. 67 ‘Apparently Harris and Marsh’ve been trying for a takeover of Chernwoods’ for quite a while now.’ ‘I always thought that dog doesn’t eat dog,’ objected Leeyes. ‘But I suppose I’m old-fashioned.’ "reciprocity