The dogs are Pascal and Ludwig, the friends of Borgman. The movie does not explain why they can take the form of greyhounds but because Borgman talks to the dogs as if they were Pascal and Ludwig we can safely assume they are the same entities. Greyhounds are the only breed of dog specifically referred to by name in the Bible.
They are actually not Greyhounds but Galgo Espagnoles.
The movie does not mention it explicitly but there are several hints pointing in the direction that they are demons. At the start they are hunted by a priest, Borgman makes a negative comment about Jesus Christ when telling a story to the children and Borgman shows the ability to seduce people and influence peoples' dreams.
