I am looking to have my Irish double checked. I believe that in Irish Thomas Gulley is translated to Tomás Ó Gabhla is this correct?

I'm not finding 'Gulley' in my (admitted limited) surname resources...maybe someone with something more exhaustive can help.

Redwolf

Irish identity has Ó Gabhla for Goaley, Gooley, and Gully.

Tomás Ó Gabhla looks about right to me (but wait for more input.)

It's not actually possible to "translate" names. Nor can you use them officially without going through a deed poll, so this would be an Irish nickname of sorts.

If you are planning to use it on an Irish passport on the other hand, I believe you need to show proof you use that name in everyday life.

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

It is your right in ireland to use your name as Gaeilge Breandán to get a passport you will need to show photo id with your name on it easyist way to get this is to get a driver licence with your name but a word of warning if somebody is going to do this they need to go the whole hog and get everything translated as if you go abroad you are going to have problems explaining why your credit card is a different name than your passport/driver license.

Yeah, I forget to clarify "outside of Ireland". MacFear was saying too that it was harder than he expected to provide that proof for his passport application - the driver's licence is definitely a good suggestion.

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).