Correct spelling for the English word "Edithe" is [ˈɛda͡ɪð], [ˈɛdaɪð], [ˈɛ_d_aɪ_ð] (IPA phonetic alphabet).
There doesn't appear to be a widely recognized etymology for the name "Edithe". It is possible that "Edithe" could be a variant spelling or a modification of other names such as "Edith" or "Edythe". "Edith" is derived from the Old English name "Ēadgyth", which consists of the elements "ēad", meaning "wealth, fortune", and "gyth", meaning "war". "Edythe" could be a variation of "Edith" with an added "y" sound. However, without specific historical or linguistic sources, it is difficult to provide a definitive etymology for the name "Edithe".