Dog end
I searched for weeks but cants find the origins of the phrase 'dog end' as in the cigarette butt
allwords.com says it's from the 1930s, but that's all. Pamela
Partridge's Dictionary of Slang asserts that it is from the 1920s and surmises that it is a corruption of 'docked end', i.e. a cigarette that has been nipped off and kept for later.
It could also be one of the many uses of 'dog' as a prefix, denoting a bad or mongrel variety of something - 'dog-Latin', 'dog's breakfast' etc.