I was wondering if whether the current Yamano_Remon is correct or is her name supposed to be "Lemon."
The character Yamano R/Lemon (山乃 檸檬) is from the series ano_natsu_de_matteru (English title: Waiting in the Summer). Sites like ANN list it as Remon and Crunchyroll is subbing her name as Remon, but I think it should also be pointed out her similarity to Morino Ichigo (森野 苺) from Onegai Teacher and Onegai Twins in appearance, personality, and VA. Ano_natsu_de_matteru's screenplay and original character designs were done by people who contributed to the character conceptional designs and scenario writing for Onegai_* series, and so it wouldn't be out of the question that when they designed Yamano that they also had her share the trait of being named after a fruit like Morino.
As I do not know Japanese, the best I can do is rely on mechanical translations, but the name 檸檬 does lead to the Lemon page on Japan's wikipedia and googling does result in images of products labeled "Lemon" in English as well as plenty of Lemon fruit pictures.
Just for completion sake, here is a audio clip of her self-introduction from episode 1.
http://www.divshare.com/download/16555804-15c (alternative direct download of file)
Updated by jxh2154