As far as we know, no one (except Zoom) knows the identity of the masked man, even if many characters spent time in the prison with him.
He can't talk, agreed. Yet he can hear and see, and can make noise by hitting the glass and make signs with his hand. It shouldn't be difficult to communicate with him (even if it would certainly be slow), and at least know his name.
As far as we know, there have not been very many other people held captive in that room with the masked man that could figure it out. (It appears that the people in the Arrowverse have yet to realize that literally everyone is Jay Garrick.)
Wally and Caitlin were unable to communicate with him in the short time they were around him. Barry eventually realized what he was saying, but did not have much time to do anything about it before he had to leave.
Killer Frost claimed not to know who he is; she may be telling the truth, since she probably didn't care at that point. But she might also have just been lying, since she seemed to react oddly to Caitlin wanted to let him out. Unfortunately, even if she knew his identity she died before telling anyone.
The only person who was there for very long was Jesse. She may have tried to talk to him, but from the way she talked about him to Barry, most likely she just assumed he was crazy. Given her predicament, she may not have even considered trying to get help from another prisoner.
Zoom himself was also strict about not letting the masked prisoner talk to anyone; he reprimanded him for talking to Barry, and proceeded to beat Barry to a pulp as punishment. So the only time anyone would have had a chance to talk to the masked man was when Zoom was away, and we have no idea how much time he spent away from his lair.
