They registered their chosen name with the Irish Football League, taking the name from the area in which they were based, Lenadoon, Gweedore, Glenveagh are all local areas named after towns in County Donegal, with the Celtic part being taken on due to the massive local following for Scotland's Celtic, and formerly Belfast Celtic.
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Donegal Celtic finished the 2004–05 season in 3rd place losing out on a promotion play-off place to Lurgan club Glenavon and also lost the IFA Intermediate Cup final on penalties to the same team at Stangmore Park, Dungannon.
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Donegal Celtic F.C., an association football club, play their home games at Donegal Celtic Park on Suffolk Road on the outskirts of Andersontown.