https://en.wikipedia.org/wiki/List_of_banks_in_the_Republic_...
so Eire has 5 significant banks, and 15 'less significant'. There are also 276 Credit Unions, I don't know if they are useful. (I had a Credit Union account in the past, could send/receive online but no payment card)
(I don't know their suitability, but there are more than 5 options in your country)
Of the "significant banks" listed, only AIB and Bank of Ireland do consumer bank accounts. I suspect the presence of the others is more to do with wanting an EU entity for targeting larger EU markets than the Irish domestic market. For example, Citibank only expanded from "large tech multinationals" to also "mid sized businesses that are planning to scale internationally" in 2023 [1]
Also on that Wikipedia page are Dell's private bank, Danske Bank (closed their Irish retail business in 2013), Klarna (sort of banking-adjacent, but they're not giving you a current account), etc.
The 5 banks offering retail consumer accounts nationwide are AIB, permanent TSB, Bank of Ireland, Revolut and N26. The first 3 are the surviving brick and mortar banks and the latter 2 are recent-ish neobank entries.
Credit unions are limited to serving customers in their local area. The one credit union who's catchment area I'm in also requires app based 2FA.
[1]: https://www.rte.ie/news/business/2023/0925/1407279-citi-to-g...
(Side note: The name of the country in English is Ireland, the name in Irish is Éire - using the accent-less Irish name in English was promoted by the UK government and BBC because they didn't want to recognise the name of the country prior to the GFA in 1998. Most people will also accept Republic of Ireland if you need to distinguish from Northern Ireland, even though that's technically not the name)