When your dog is cremated you do get your dogs ashes back.
However since more than one dog is cremated in the same dog cremating furnace you may also have some other dogs ashes mixed in with your dogs ashes.
The dog cremating furnace is usually cleaned out fully or at least as much as possible between cremations of dogs and pets but sometimes a little bit of ashes from other dogs and pets can still remain in the cremation furnace.
So it's possible for some other pets ashes to get mixed in with your dogs ashes.
So while you do get your dogs ashes back when they are cremated you may also have some other dogs ashes or other pets ashes mixed in with your dogs ashes.
There's not much of anything the dog or pet cremation place can do to fully prevent that.