I hope this makes sense. I have the following information for Anne (Maria Anne) Morgan:
Birth: 26 FEB 1896 North Marsh, Dundalk, Louth. Parents: Bernard Morgan and Catherine Mills.
Census: 31 Mar 1901 Mary Street, Dundalk Urban No. 4., Louth.
http://www.census.nationalarchives.ie/pages/1901/Louth/Dundalk_Urban_No__4_/Mary_Street/1562053/ Marriage: 16 MAR 1920 St. Patrick's Church, Dundalk, Louth. Husband: Peter G Dunne. Father: Bernard Morgan.
Shipping Manifest: 31 AUG 1921 Mary Dunne, 9 St. Mary's Terrace, Dundalk. Departure from Liverpool to Philadelphia.
https://www.ancestry.co.uk/imageviewer/collections/2997/images/40610_B000944-00008?pId=47252404 I just got her death record, and her parents are listed as Henry Morgan and Mary. I'm positive it's the same person, as I've all the above paperwork plus documents for her three children, she died after giving birth her fourth. Also, I've found a marriage record for Peter Dunne, Widower, from Dundalk, same age and US address, in 1928.
Bernard's father was called Henry and his wife was called Mary. Also, Bernard had a brother called Henry, b. C 1867, who married with a Mary. I wonder whether Peter made a mistake when he filled in her death records? I'm almost certain I got the right Anne, but would appreciate a second pair of eyes.

I want to add that someone on a different post kindly pointed that there's a grave for a Bernard Morgan that well possible could be him. However, there's a mention of a daughter called Anne Donnelly who passed in 1969, while Anne (Dunne) died in 1926.
https://billiongraves.com/grave/Henry-Morgan/10861260