... strange but true - possibly originally a corruption of the Isle of Doggers (the "dogger" being a Dutch fishing boat way back when), the Isle of Dykes (an embankment/flood bank) or even the Isle of Ducks thanks to the marshland habitat which ducks favour.
Another "Island of dogs" is of course The Canary Islands (from the Latin, Canariae Insulae) named because of the packs of wild dogs that used to roam the place ... which in turn also references Canary Wharf back home - nothing to do with Tweetie Pie - named thus because of all the imports of fruit from The Canary Islands.
After all that, surprised the film wasn't entitled Dog Isle or Dog Island to avoid confusion (lol).
Isle of Dogs... was said to have been where Henry VIII - among other kings - kenneled his hunting dogs ... although looks more like a peninsula ... despite the man-made waterways leading off West India Dock ... w/ another less palatable theory behind the name of the place is that dead dogs - as well as other dead things including humans - washed up there on an adjacent sandbank.