Do you mind sharing the name? And it wouldn't bother me.
I'll be honest, I don't love the name, it just makes me think soup, BUT I wouldn't not use it (do I have too many double negatives in there?) just because it was the neighbor's dog name.
In fact, one of my mom's best friends has a dog that has the same name as our son, and I didn't even hesitate to use it, even though that dog will probably be in our lives for his whole life. We even joked about it when she found out the name of our son:
Her: Ohhh I love that name!
Me: I figured it would get your seal of approval.