Hello again Mark!
I'm including your Mary 20th message here for the information for other volunteers https://irelandxo.com/ireland-xo/message-board/searching-peter-kane-born...
I tried to find the full page of the parish register to get a broader view but for some reason, I can't find the record that you have in the screen shot.
I believe that the word after Mary Bird is actually a place name not part of her name.
There is no way at this point to make a reasonable conclusion that this Peter Kane is your ancestor. You would need some evidence that shows his wife was Mary Bird possibly DNA matches who have Bird connections. Baptismal records for children which shows parents names etc.