I think a common trait of people who frequent this board is that they enjoy research! I love to talk about Japanese names, and rarely get the chance.
Yes, I do find
Rene as a Japanese girl's name, although none of the examples include the meaning "lotus." No reason why you could not use that character in the name, however.
Here are some meanings of
Rene:
伶音 actor + sound
玲音 clear, sweet (sound) + sound
礼音 manners, etiquette + sound
礼子 manners, etiquette + child
礼寧 manners, etiquette + peaceful, tranquil
麗音 beautiful + sound
恋 love
恋音 love + sound
澪音 waterway, channel + sound
I would not know if one of these is more common than another. I think
Rene is a rare name in Japan and most likely borrowed from English/French.
Miren is also comparatively rare; Renna appears to be considerably more common.
Some meanings of
Ren are: lotus; love; actor; wise; clear, sweet (sound); manners, etiquette; bell; beautiful.
Meanings of Na: name; summer; vegetables; south; pear; as well as a character 奈 very commonly used in names which no longer has a distinct meaning but is used for its phonetic value--it is the "Na" of the city of Nara.
Meanings of Mi: beauty 美 (one of the most common characters used in modern Japanese girl's names); reality, truth; 8th zodiac sign (the year of the sheep, 2015); charming, bewitching.
You can mix and match any of these as you choose, just as Japanese parents do!