You can call your dog whatever you want.
Many, maybe most, dogs enter a shelter environment as strays with nothing whatsoever (including their names) known about their history. The shelter may give a dog a name to be called by while the dog is there, but it’s probably not what they were originally named by an owner. Two of my rescues were listed only by their kennel numbers (no names) so they certainly got new names!
My current dog (also a rescued stray) was given a name by the shelter, but it was weird and didn’t fit her. She was also renamed and it took no time for her to recognize and respond to it.
A new name can also mark a new beginning. Every adoption means a new (and hopefully BETTER) situation for the dog, so why not a new name, too?