Worth noting here is that Shannon's use as a given name started and predominates in the New World (It may now have some more modern usage in England and Ireland).
Shannon falls into the group of names such as Colleen, Kerry, Tara, Tyrone, and of course Erin (Desmond may belong here as well, but debatably). Their roots are from the Gaelic language, but they have never been used as given names in Gaelic, nor in Hiberno-English. Through the years the Irish of America (and Canada & Australia), especially those who knew they were not returning, named children in ways that were evocative of their homeland, but were not in lines with traditional naming customs. Kerry and Tyrone are county names, Tara is the storied seat of Ireland's kings, and Colleen is just the word for girl. Now the Shannon is a river that almost always has the 'the' attached to it, even in Gaelic the word is "An tSionainn."
So while this website's attribution of Shannon solely to the English page may be an oversite (Shane and even Barclay are included among the Irish), it does have a tenuous connection to the Irish of Ireland.