My Chinese name in Japanese?

Hello! So my name is 雷 夢媛 and I was wondering how to read it japanese
I take that my surname would be read as ライ instead of かみなり
Now the problem is my name. I've been reading that most people uses the chinese reading , that would
be メンユエン or onyomi むえん
Reading it as it's normally read and not properly feels weird and in onyomi sounds to me even weirder(maybe it's just me)
How usual is for foreigners to do their reading in kunyomi?Mine would be ゆめひめ. Does it sound strange?
In Hipenpal my name appears as ゆえ, which is quite normal
I personally like ゆめひめ orゆえ. And I take that anyone is free to choose how they want to be called but would it sound strange?
Opinions anybody?
And thanks :D

Like you said, it is your name so it is up to you to decide how it is read. Here are some comments for each option:

ゆめひめ - Hime, as you probably know, can mean princess (姫 is also read hime). So when you present yourself as ...hime, that sounds a little funny (might be taken as being arrogant). It is one thing if your friends give you a nickname Yumehime, but quite another if you ask your friends to call you ...hime. But if you like being called a princess, go for it. I would write it in katakana ユメヒメ.

むえん - If you present your name 夢媛 in writing, this is probably how most Japanese would GUESS your name, because it is in on-yomi form which is the most common way for a Chinese name. But don't write it in hiragana, use katakana ムエン. Because there is another word 無縁 which is also read むえん.

ゆえ - I cannot find any potential controversy with this name, so it may be the best compromise.　　But I would write it in katakana ユエ.

Not sure it's such a good idea to post your full name online ...

But anyway, with Chinese names, I find that in Japan they tend to follow the modern Chinese pronunciation, not on-yomi. Of the three possible pronunciations you offered, I think "Yumehime" would be the least preferred, although not impossible if that's really what you wanted to go by. (Mu-en is also not great because it sounds like a homophone for 無縁) But it would be strange to read your last name in on-yomi and your first name in kun-yomi, and to be quite honest, "Yumehime Kaminari" sounds like a character from a manga or something (and some may mistake it for being a very odd Japanese name and not Chinese.)

So all told, I think going with the pronunciation that is closest to the modern Chinese is the best option.

"with Chinese names, I find that in Japan they tend to follow the modern Chinese pronunciation, not on-yomi."
That's not always the case. I know more Chinese people that follow Japanese on-yomi than Chinese pronunciation rendered in katakana. It's kind of arbitrary in fact.
To make a famous example, Chinese figure skater Jin BoYang 金博洋. When they show competitions on TBS, they call him ボーヤン・ジン but on Fuji and NHK then call him キン・ハクヨウ.

That is true; there is a large degree of flexibility in these cases. I was only speaking from my personal experience with Chinese friends and coworkers.