Irish surnames

What is an Irish Surname?

First of all, we have the question "What exactly is an Irish surname?" Is it a name which originated in Ireland and was only ever found in Ireland? Is it a name as gaeilge (through Irish)? Is it a name which was brought in to Ireland with the Normans? Or does that remain a name of Norman origin, which is found in Ireland.
If a person tells someone that their Grandparents came from Ireland and that story is handed down through generations for 300 years and then some member of that family decides to trace their ancestry - and they just know that
their ancestors came from Ireland, and they ask a question somewhere - a mail list, a message board or at a genealogical society meeting and other people tell them "That is not an Irish name because it is not found in the Mathesons Report on Irish surnames and it is not found in any of the books published by Edward McLysaght", then I ask you what is the descendant to do?

If they are told that the name is found in England, Scotland, Wales, France or Spain, but not Ireland, by those who possess the publications I've mentioned, where do they turn? If their ancestors said they came from Ireland, then to my mind, those people must have been born in Ireland regardless of where their parents or grandparents came from.

Let me give you some examples, Easy enough to spot the variations
Achmooty* /Aughmuty* /Aghmuty /Ahmuty /Auchmuty
Ahearn* /Aheran /Ahern /Aherne* /Ahearn* /Aheron
Archdeacon* /Archdekin /Arcedeckne /Aercedeckne /Arsdekin /Arcedeickne
Bagnall* /Bagnel /Bagnell /Bagnal /Bagenal
Bailey* /Bailie/ Bailie*/ Baillie/ Bailly /Baily /Bayley /Baylie /Bayly*
Barber* /Barbor/ Barbour*
Daily/ Daley/ Dally/ Daly* /Dawley* /Dalyly
Delahayde /Delahide/ Delahoide /Delahoyde

With a bit of guesswork:
Eayres/ Ayres* /Eyres/ Eyre*/ Ayre*
Ellard*/ Aylward* /Elliard
Fair* /Phair* /Faire
Fay* /Fee*/Foy*/Fey*/Fye*
Archbold* /Archaball

And then we come to the difficult ones, the names which sound the same but
look different.
Adlum/Odlum - easy enough
Agar/Eagar - not too bad either
Aghoon/Whitesteed - McLysaght says so, different counties!

and if you click on this link you will find the full article plus links to some surnames sorted alphabetically A-J (about 4,000 in all including variations)
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