I'm not a big fan of anthropomorphizing pets. Dogs is dogs, they ain't people. Treating a dog like a person is unhealthy for the dog and crazy-making for the human.
That said, a few years ago after I got my dog from the pound I guesstimated a birthday for her, and every year my computer reminds me that it's her birthday. I don't do anything wildly special for her, but it's a nice excuse to remember to do something nice for her, in a life busy or draining enough that sometimes I forget to play with her enough or take her for enough walks. Yesterday I happened to be at a pet store buying her the dog food she'd run out of and right next to the register there was a little doggie cupcake, so I bought one for her. And in the evening we went for a sidecar ride down to her favorite cafe. As we sit there, her watching the people and my writing on my laptop, people come up constantly to pet her. I tried an experiment and told every person who came up that it was her birthday. It was amusing and heartwarming to see their reactions, people were extra nice to her extra excited to see her, and seven people bought her dog treats (they sell them at the cafe). I think that was a new record for her, in terms of people buying treats per hour. Her previous record was 13 people in one evening buying her treats, but that was over about 5 hours (and this time it was in just 2).
Ah, the life of a loved dog... If the Buddhists are right and I'm good enough this go 'round I hope my next reincarnation is as kind to me and as furry.