I've mentioned the Alan Moore's League of Extraordinary Gentlemen a couple of times (see Rider Haggard and HG Wells adaptations). I didn't make the connection at the time, but now I recognise poor old Bonzo as the failed experiment H-216 dead on Dr Moreau's slab in League of Extraordinary Gentlemen 2. The Moreau page at Damian Gordon's League of Leagues site identifies various other animal characters in that segment, including those from The Wind in the Willows and a number of others I'd scarcely heard of, such as Toby Twirl.
Nobody knows where the dog's name "Bonzo" - thought up in 1922 by Bruce Ingram, Studdy's editor at The Sketch - came from. However, the name appears to have been quite a popular meme inthe previous couple of decades. Puccini's Madame Butterfly has an Uncle Bonzo; this because the Italian "bonzo" (English "bonze") is an archaic name for a Buddhist priest deriving from a Portuguese import from Japanese (an unusual etymological path deriving from the Portuguese being the sole Western trading contact with Japan in the Shogunate period in the late 1500s). There was a Colonel Bonzo, a main character in Pemberton and Fleming's 1908 play The Woman of Kronstadt (based on the novel serialised in The Windsor Magazine and Munsey's Magazine in 1897-8), as well as one in the 1913 play The Shepherdess Without A Heart and Sylvanus Cobb's 1892 novel Ivan the Serf.
"Bonzoline" was also a patent composite plastic formulation for billiard balls from the late 1800s - see The Global Snooker Centre - leading Punch to postulate the Bonzo in a spoof article about billiards:
Ivory balk held the field until the opportune discovery of the bonzo in the forest of Swami by the late Sir H. M. STANLEY. The explorer came suddenly upon a huge herd of them in a clearing. The creature is practically all tusk, the merest thread of body with several hundred-weights of the hard glistening material attached to it. No sooner did the bonzos see STANLEY than they made a huge break for cover a happy augury. The herd, however, moved but slowly owing to their wealth of bonzoline (as it is now called), and it was an easy matter to round them up and secure them. Bonzo ranches now cover the Swami district and large fortunes are being made. Not only are the bonzo's tusks (which, we ought to explain, it drags behind, having insufficient strength to carry them) useful for billiard balls, but excellent false teeth almost like real, are made from them too, and the best professionals wear no others. Ex-President ROOSEVELT also keeps a set by him, in case of accident.
- Punch, April 26, 1911, p.309 (Internet Archive)
Interestingly, Ingram/Studdy must have been well aware of the term "Bonzoline", as it's used in a number of the Bonzo captions such as the one for this picture ("Bonzo shows the Bonzolines how to do it" - where "Bonzoline" appears to refer to other Bonzo-type dogs) and others mentioned in the sketch list at Studdying with Bonzo ("The Bonzolines 'have a couple'" and "The Bonzoline has a sweet tooth"). If I had to bet on an inspiration, I'd go for Bonzoline.
However, one could speculate forever. I'm sure it's coincidence that "Bonzo" could be read in some kind of semi-Latin as bon zo (= good animal), or that there was a Creole proverb "Bon chien pas janmain trappé bon zo" (= "a good dog never gets a good bone"). But whatever the origin, it was an inspired choice for Studdy's characterful little bull terrier pup.
Addendum: Julie Heyward just sent us a YouTube link: Bonzo in Tanked. Thanks!