The owners name can be found in the municipality license certificate inside each shop, Still this will not make a difference . Many of those owners can be old men or women , who were encouraged by the goverment to open pets shops. Some of them might have never visited their shops and just receive the monthly profit
I think The best solution would be that the animal resources department take up this subject and their vets uses the law enforcement authority given to them by law.
Few months back, they did crack down the camel souk after some cases of livestock mortality were reported