I think a Chinese speaker might better answer these questions for you, as, correct me if I'm wrong, but the aesthetics of the name depend in part on how the tones for each part of the name sound with each other. Just putting two hanzi symbols together might lead to a good meaning or something that looks or sounds nice in English, but doesn't work as well in Chinese. I might be wrong, but if not, a Chinese-speaking friend might give you more accurate opinions and ideas. You've probably asked them already, though.
I don't know what your surname-based name is, and wouldn't ask you to reveal it, so I can't comment on it.
I like 'Happiness Orchid' better than '
Lotus Orchid'. The latter is too flower-y, and the former feels more descriptive and therefore more natural.
One avenue that might be worth looking at is taking inspiration from the meaning of your name.
Francesca means 'French', and the interwebs tell me that the Chinese for French/France is 法国人/法国. 法 (Fà) doesn't only mean '
France' but 'law, dharma, rule, way', so if
Fu doesn't work, maybe Fa could be an alternative, if it's used in names. Eh, that idea sucked a bit, I must admit.
So, I tried finding inspiration from Chinese/English names of celebrities:
Ideas:
Based on F-
菲 (Fei). It means 'humble' and is the Chinese name of
Faye Wong. I don't think the meaning's great, though, as it can also mean unworthy.
芬 (
Fen)? This is also Fang, apparently.
法拉 (Fa La)? Like Fala
Chen. Admittedly the meaning isn't stunning and the name doesn't work amazingly in English.
风 (Feng)? (Wind, as in, air, I imagine, style)
Based on C/Ch-:
Ching/
Jing - 瀞 - Ching may be a regional pron.
Chang?
Zhu (朱) - sounds like Chu - means 'scarlet', 'vermillion', and is kind of cool.
Chun?
Chin? (
May be the same a Ching)
....
And then I lost interest. But I did stumble upon the fact that Q in pinyin often = 'ch' sound. It might not fit with how you say your name, depending on whether you use 's' or 'ch' on the second syllable, but it opens up a world of other options - 啟 (Qi/Chi, meaning beginning), 青 (Qing/Ching, meaning green or blue, I think this one is very pretty. Would Ching Lan/Qing
Lan work? Blue Orchid would be pretty), 秋 (Qiu/Chu, meaning autumn), and so forth.
I mean, it doesn't have to fit perfectly with your English name, does it? When Anglicizing Chinese names, anything seems to go, so you probably have a bit of leeway if you want it when doing the opposite.
I kind of went on a tangent, and I doubt anything I wrote helped any, but, hell, maybe it wasn't -unhelpful-.