Hi Albert,
I understand the need to have an artsy name, but both names, especially "Fallen Lotus Petals" sound incredibly fake. Alas, these types of names would be acceptable in a fantasy world, though not be realistic. Such artsy names are common in cartoons, anime, movies, etc. Realistically, monasteries wouldn't condone what you're suggesting they be used for...they're like churches in a sense... China has a lot of mountains and quite a few of them are named after said mountains. Most Chinese (Buddhist) monasteries are not translated into English, but rather uses Pinyin instead. The exception would be the Badachu 八大處 "The Eight Extraordinary Places" in Beijing and the norm, Hanshansi 寒山寺 in Jiangsu Province.
A list of important Buddhist monasteries in China can be found here at the bottom of the page:
http://www.chinaknowledge.de/Art/Pagodas/pagodas.html
Good luck,
Gryffindor_Slytherin