It all depends on what you mean by 'elegant'. I think of someone like the designer Jean Muir - strong shapes, pure lines, no frills, no fuss, no irony....
Following that, the sort of names that follow are plain, strong and simple.
Jean (as above) or Joan,or Jane, Mary, Honor, Faith, Agatha, Agnes, Margaret, Elizabeth, Anne/Anna, Helen, Judith, Bridget, Catherine, Emma....there are others.
Latin and ancient Greek names can be elegant, but not if they are fussy.
Absolutely no names ending in 'elle' or 'ella'. No supposedly 'unique' names (no name is unique unless freshly-minted) .
No European or other culture names names suddenly discovered and used out of context: Eloise, Ottilie etc. Brilliant if they are from your heritage, but otherwise...
Very very sorry if this sounds impolite.