For trademarking, you can go to the Irish patents office site (hence the misunderstanding I presume) and do a search on the trademark to see whether it is already registered.
Assuming this is clear, you can apply for a trademark using the Patent Office application form.
Be advised that you must have everything correct on the application as you will be in for an extremely frustrating time with the patents office. I originally applied for trademark protection on my logo and product names over six months ago, and it has been extremely frustrating up until now (still in process). I submit, some time later I get a response to ask to change wording (of an extremely pedantic nature), I do this, resubmit, then get letter back to change a different set of wording (which was also present on the original submission), and to and forth. Although the trademark officer has email, they will not use this to communicate any information.
Fortunately, if you have made an initial application and it is subesquently approved, you are covered back to the date of the original filing.
If you want to file for an international trademark, you need to file first in Ireland, and once it is accepted there, you can then apply to have it applied to other countries.
Note also that while doing this yourself is tedious, the costs of going through a patent attorney is astronimical. I think I have saved approx 11k by processing the four trademarks myself.
If however you are applying for a patent down the line, I would definitely use a patent attorney, as this is not something you could or should do yourself