Hibernia
The name of the Irish language in the English language is ‘Irish’.
Gaeilge is the name of the Irish language in Irish.
Either of these would be acceptable.
‘Irish’ would fit in better in the list of languages.
Gaelic is spoken in Scotland. Irish and Scots Gaelic are quite different.
Scots-Gaelic & Manx are in the same family of languages as Irish Gaelic - but Manx is actually closest to Scots-Gaelic than Irish Gaelic.
A bit like Estonian & Finnish, & Faeroese & Icelandic - same families of languages, different languages, but can be understood to a certain degree by each others' native speakers.
Aidan.