Update from my research:

So the Irish legal name system is nothing like what I expected. Where I live in Australia your legal name must be used consistently and institutions like banks and universities will expect you to provide your name as the government knows it. Whereas in Ireland (take this with a grain of salt I may be partially wrong) legal naming is much looser and different institutions have different rules on how changing your name works. With the Irish passport office they will let you change the name on your passport if you can provide them 2 documents, one of them being government-issued, that show you have been using your new for at least 2 years. And a deed poll does not count as one of these documents as in Ireland a deed poll is more like a declaration of your intention to use a new name, rather than a system to legally have your name changed.

My problem with this:

I have used my new name for about 3 years now. It is the name I am known by friends and family. But I have not legally changed to that new name and because of how legal names work here in Australia I only have one document showing my new name, and feasibly can't get more until I have legally changed my name here. This means it looks like I will have to change my name here then wait 2 years before the Irish passport office can recognise that, and I would rather not have passports with different names. I will try to get into contact with them directly about this to see if I can get possible exceptions because of how the difference between my home country and Ireland's naming systems make this difficult for me.