Gaiscaíoch means a "hero" or "warrior" and sounds something like "Caiseadach". I've read that the surname "Ó Casaide" may mean curly-haired. A "cas" is a turn or a bend, so curlyhaired is plausible.

Notes from The Doegen Recordshttps://www.doegen.ie/LA_1248d2:

    "These verses are most commonly sung as part of the well-known song ‘An Caisideach Bán’. Mary Costello (Galway) and Pádraig Ó Néill (Galway) sing Connacht versions elsewhere in the Doegen collection. Cathal Goan notes that the verses on the present recording and verses from ‘An Draighneán Donn’ and ‘Mailí Mhómhar’ are often found together in Donegal, where the song is known as ‘An Gaiscíoch Bán’ or ‘An Buachaill Bán’. See Cathal Goan (ed.), Róise na nAmhrán: songs of a Donegal woman (RTÉ, 1994), 39. Róise Bean Mhic Grianna (‘Róise na nAmhrán’) sings it under the title ‘Dá mBeinn i mo Bhádóir’ on the accompanying CD. Éamonn Mac Ruairí (Tory Island) and Áine Uí Laoi (Gaoth Dobhair/Gweedore) sing Donegal versions on Seoda sean-nóis as Tír Chonaill (Cló Iar-Chonnacht, 1996), where introductory notes and texts are provided by Lillis Ó Laoire. Ó Laoire (personal correspondence) notes that in Donegal versions the phrase ‘An Buachaill Bán’ is most often used instead of ‘An Caisideach Bán’ (see end of the second verse in the present recording). Altan include a version of the song on Celtic myths (Proper Recording Arts SA, 2002)."

The above paragraph is quoted at https://songsinirish.com/thug-me-ruide-lyrics/ as is the anonymous guest's 9 Dec 2004 comment on this discussion thread - with no mention of the Mudcat Café. You can disregard the abysmal machine generated translation on Songs in Irish page, and "Cruaiche" is the correct spelling not "Crudiche" (it may have been cruadhaiche before the spelling was modernized?). Also in the first line of Thug Mé Ruide, Mullaigh or Mullach are both acceptable.