The original grant of arms will definitely say who it was granted to.
I have one here - in this case it was a surname becoming double-barrel after a nephew was named heir to his uncle, he appended his uncle's name onto his own. It states his relationship to the uncle but is mostly about the design of the arms.
There is currently no chief herald of Ireland, and I believe they do not plan to replace him. So if you were to go to the NLI, there wouldn't be someone who could "confirm" the connection. The happier news is that since there is no chief herald any more, you won't be subject to his whim and should have no problem getting to see the original grant. Until his retirement, he could decide whether or not to let someone see an original and most of the time didn't!