I used to think it was just a thing that uninformed Americans did, but I was wrong, so let's talk about it.
There are Irish people (notably, native Irish speakers) who call it "Gaelic", when speaking English. (All video clips are timestamped, but it seems like timestamps don't work on mobile? So I'll write them as well)
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4:36
In the name for the language in Irish varies across the dialects, but in Donegal, it's usually said as "Gaeilic"*, as you can hear here. (Bhí an Ghaeilic thar timpeall achan áit)
It's fine to call it "Irish" as well, or "Irish Gaelic", but there's nothing wrong with just saying "Gaelic".
Notes
*I spelt it as Gaeilic for the sake of showing the pronunciation here, but really this comes from Gaeilg with the final consonant being devoiced in a similar way to how you see with Pádraig -> Pádraic
Some people will argue that you shouldn't call it "Gaelic" because there are several Gaelic languages, and it lacks specificity. It's true that it lacks specificity, but that is also how they're spoken about in the Gaelic languages themselves, e.g. "Gaeilge na hÉireann, Gaeilge na hAlban, Gaeilge Mhanann" (The Gaelic of Ireland, The Gaelic of Scotland, the Gaelic of Man) in Irish. There was, and still is to some degree, mutual intelligibility between these languages/dialects and it should be remembered that the difference between language and dialect is largely political.
is FUATH liom bliain sagam bí ciúin faoi teifigh 💔💔 “feel like a foreigner in my own country” agus chonaic sé turasóirí le dáth craiceann difriúil like socraigh síos….