Just a small point. When written Margt, Mary and May can look similar.
Do you have a copy of the document which names his mother as May? It could be worth getting a second opinion on what is written.
As that information was presumably given by John himself, then you would expect it to be accurate, however accents and what the person who filled in the forms believed John said, need to be considered.
I might be trying to make this fit, but I can see there could be a similarity between the spoken Wright and Reilly/Rahiley.