Mandarin
Lan for "orchid" is more exactly lan2 or lán as written in Pinyin (a system to write Chinese with Latin script) because the "a" is spoken in the second tone, means the tone rises.
Strictly speaking the name does not mean "beautiful orchid" but simply "orchid". To add "beautiful" would need another syllable and give a name like Meilan (which seems to be in use as well). But of course an orchid is supposed to be beautiful.
The Chinese character for orchid is: 蘭
You find details about this character and a picture to properly display it in case that your computer does not have a font installed that includes Chinese characters here:
http://www.unicode.org/cgi-bin/GetUnihanData.pl?codepoint=862D
The long horizontal stroke at the top crossed by two small vertical strokes is the radical for "flower" and tells us that this character stands for some kind of flower. The rest of the character below this is: 闌
http://www.unicode.org/cgi-bin/GetUnihanData.pl?codepoint=95cc
The core meaning of this character is some kind of fence to bar entry to some place. As such it has nothing to do with flower in general or orchid in particular; it just happens to stand for a word that is also pronounced lan2.
You can further decompose this character into 門 (gate) and 柬 - see
http://www.unicode.org/cgi-bin/GetUnihanData.pl?codepoint=9580http://www.unicode.org/cgi-bin/GetUnihanData.pl?codepoint=67EC
In the Chinese mainland you would hardly see this beautiful but somewhat complicated character for orchid because it was replaced by a "simplified character": 兰
http://www.unicode.org/cgi-bin/GetUnihanData.pl?codepoint=5170
But in Hongkong, Taiwan and Japan they still use the traditional character that I explained.
Rene www.AboutNames.ch