You can put double barrelled names in Irish, all right
More information ->
http://www.nualeargais.ie/gnag/gram.htm On that page it explains about a particular form of surnames that can be used. It's used in a similar manner to the English practice of calling someone by their surname. For example "Smith", in the sentence "Smith came in earlier with those documents". So it's a way of referring to someone without using their forename.
Someone named Eoghan Ó Ceallaigh could be referred to as "An Ceallach". Muiris Ó Modhráin would be called "An Modhránach". The grammatical rules for forming this name are on that page mentioned above. I believe Mac Thomáis would go to "An Tomásach". How this is relevant to double barrelled names is also explained on that page. Basically, you take the first name in the surname and put it in that form and then leave the second as is. So I believe it would come out as "Antóin Tomásach Mac Cormaic". Of course you don't have to use that, if you like your current way better. I have a double barrelled name myself and I tend to just use the first part in Irish.
I hope that this explanation made some sense, apologies for anything that wasn't clear!