I actually haven't ever heard anything offensive or racist, but the number of dogs I meet that are named Bella pisses me off. In general I'm not too fond of human names for dogs, but it really depends on the dog.
One time I jokingly suggested that we name this mini Aussie at the rescue Roger, but I was taken seriously and that's what they named him. And when he got adopted, the owners kept the name.
ETA: And we often get bizarre names from dogs coming from California. One of the most memorable ones was Mr. Buggles.