Let me tell you a secret!
Irish Gaelic is not called Irish Gaelic by Irish people in Ireland.
It’s nice that we could get that out of the way. So if you’re looking for another name for the Irish language, you can begin with “Irish“. Many Americans have said that this sounds unnatural to them, but it is how the language is called in Ireland.
For example, it would be perfectly natural in Ireland to ask someone “Do you speak Irish?”, or “I learned Irish in school”.
And be sure not to call the Irish language simply “Gaelic”. While some people in Ireland will refer to the language like that, it’s an ambiguous term. This is because there also exists Scottish Gaelic, which is often simply referred to as “Gaelic”.
Another Name – How the language calls itself
When speaking in the Irish language, you call the language Gaeilge. Pronunciation of that word does vary between regions of Ireland, depending on the dialect of Irish. Even another language for Irish Gaelic is “Gaolainn” (you’ll see several spellings of this) and it’s a variation only used in the south of the country.