There are 3904 Egan records on Griffiths!
And 1491 Egan records on the The tithe Applotment books
Hours of fun!
ETA I think looking at Annie's hesitant signature on the marriage document that she may not have been fully comfortable with reading/writing and therefore not able to correct a mistranscription of her name.....bearing in mind she would have had an accent and people writing records for her would have written what they heard. This may not been the way it was often written in the country of origin.
Thank you Aghadowey for the tip about possible spelling of the name in Ireland.
Right about the Egans. I forgot the lady was from Tipperary and was only looking in Shankill, because that is the only place that Steen and Eagan were both found on Griffith's Valuation. - Not sure about Steen and Egan - I don't know how John Grenham's surname search handles sound alike names.
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Regarding Annie's signature, a possible match for widow Annie (Agen) Golden on the 1870 census. said she couldn't read or write English.
https://www.familysearch.org/ark:/61903/1:1:M8D1-R7S----
There were a few other Agens in New York at the time, so she wasn't the only one spelling it that way. Not to say that they all couldn't have been Eagan or Egan somewhere else.
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Still no closer to finding her death and burial in the US or her Irish origin, though.