Wow, well, my son is called Rex. He is four and we have only ever had one bad reaction to his name; a woman who wrinkled her nose and asked why I named my son after a dog. Her son was called Tyson, after the boxer so we have different tastes anyway.
Now, I know that people say that people always say what a lovely name it is after the baby has arrived. That isn't strictly true; my daughter's name had several bad reactions (and no, she's not called Patch!). Also, we often (at least once a week I would say) have people going out of their way to comment on what a lovely name it is.
It isn't that uncommon anymore. We know of three others (we are in rural Yorkshire so hardly a cosmopolitan region) and it is 212 in the latest stats with 266 baby boys called Rex in 2015, I would imagine it will have risen again when the 2016 figures come out later this year as it has been rising sharply since 2010.
names.darkgreener.com/#rex
Yes, it was once seen of a traditional dog name and of course some people will still have those associations but it isn't a popular dog name now. It was also a human name a long time before it was used as a dog name, it was first listed as a given name (for humans!) in the early 17th century so certainly has long history.
It is absolutely fine not to like it (there are loads of names that I don't like!) but to call it cruel or a name for a dog is simply inaccurate now.