As an English name, it has been used occasionally since the 12th century. It is the name of a central character in Shakespeare's play The Two Gentlemen of Verona (1594).
As a Russian name, this is an alternate transcription of Людмила (usually rendered Lyudmila).
Regarding 伊織, it belongs as an 'azuma hyakkan' (東百官) name, in which they are like hyakkanna (百官名), a court rank-style name that samurai used to announce oneself and give himself authority, but come from the names of government offices in the Kantō region.
The combinations, apart from the first one and the ones with 3 kanji, are unisex. The first combination is mainly used on males (albeit rarely) and the combinations w/ 3 kanji are used on females (albeit rarely).
Iori (庵 & 伊織) is also used as a surname.
This name was fairly popular at the end of the 19th century and beginning of the 20th. The American author F. Scott Fitzgerald used it for the character of Daisy Buchanan in The Great Gatsby (1925). The Walt Disney cartoon character Daisy Duck was created in 1940 as the girlfriend of Donald Duck. It was at a low in popularity in the United States in the 1970s when it got a small boost from a character on the television series The Dukes of Hazzard in 1979.
Allegedly it is sometimes used as a Hebrew form of Sophia, and is also the Yiddish form of the Judeo-Spanish name Buena.