Do newborns vampires have vampire teeth?

A new-born vampire would be called a Dhampir.

No. In fact most vampires do not have vampire teeth. The thing about vampire teeth is a consequence of Count Dracula who, besides being a vampire, was a high level sorcerer as well and could alter his physical form. He could change into a bat, a dog, a mist, a horde of rats, etc.

Before count Dracula no vampires had fangs and they go at their blood by messier means.