I've been indulging in a bit of linguistics. Names and words may have similar spellings but have different pronunciations. When I first saw this name AGNETHA from ABBA I looked upon it NOT thinking of the name Agnes but the last four letters of the word Lasagna Laz-ahn-ya. So I said "ahn-ye-thuh. The only thing most American English speakers don't understand is "TH" in unvoiced form was a character formerly called an "eth". Upper case it looks like a capital D with a sort of Hyphen through the spine of the D and lower case "eth" looks like a lower case d with a sort of cross at the top. It had two pronunciations, One like the TH in THING and the other like a TH and D sort of combination making the unvoiced TH come off of the back of your upper two front teeth. This is a hard "eth" Now, try pronouncing "ahn-ye-thuh's" name using that hard "eth" for the "TH"
Despite having loved ABBA for some time, I'm still not sure on the pronunciation. On ABBA In Japan, Agnetha Faltskög gave the pronunciation of her name, then said you can say Añeta (ann-YET-a) or Anna. The only trouble is, Añeta and the pronunciation she gave sounded the same to me!
While the name Agnes sounds nice in Scandinavian countries, I can't stand this name at all. It's hideous, sounds very dated, and reminds me of Abba (bleurgh!).