I've never heard of the name Madori, but according to some Japanese baby names websites (e.g. 1, 2) it can be a Japanese female given name. A(n incomplete) list of various kanji representations is given in the ENAMDICT database (via jisho.org).
In any case, given the rōmaji transcription of a Japanese name (e.g. "Madori") it's usually impossible to say whether a "meaning" is correct. This is because names can be written with many different kanji (Chinese characters) and these determine the "meaning".
(Sometimes parts of the name are standard, which makes it possible to make a reasonable guess on its meaning. For example, -ko in Akiko, Mariko, Yōko, etc. should be 子 "child".)
Some names also use kanji, which are likely used for sound rather than meaning:
This is likely a phonetic kanji representation of Madori, the individual characters meaning "hemp", "metropolis" and "Japanese pear".
Others, like 万鳥 "a thousand birds" (actually 10,000), are probably intended to carry more meaning.
I don't know which characters were used to derive the meaning "angel of the sky"; I can't even make a far-fetched guess. In any case, without the kanji representation, it's not possible to say anything definitive about the "meaning" of a name.