串 chuàn means "to string together" — a
串串 chuànchuàn is a skewer (the same word appears in
串串香 chuànchuànxiāng, Sichuan-style stick hotpot). A
串串狗 is literally a "strung-together dog" — a hodgepodge of breeds. The word is affectionate, not pejorative.