My partner who is from Eire has always been known as Aine and on all her legal docs it shows Aine, yet on her birth cert it shows Anne - Is this a problem, especially as we are getting married in September and we need to show docs to registrar.
No. My mother was originally Clara but known as Clare all her adult life. She was shown on her marriage certificate as Clare, since that was her name as far as the world, and the law, was concerned. It never had presented any difficulty. (Her estate lawyers, on her death, put 'Clare given as Clara on her birth certificate' out of excessive, and somewhat misleading, caution, in some of the documents!)
I don't know about Eire, but in the UK you can call yourself anything you like, ( except for the purposes of fraud). If you use a name different from the one on your birth certificate, and someone challenges you, it is sufficient to show that you have been known by the unofficial name for however-many years.
Presumably she has a passport in her Irish name ? Is this not sufficient ?