What a stressful start to your day! My situation isn't as bad as yours, but I can I understand some of your frustration.
There's another author called Andrew Butcher, and the librarians on Goodreads keep putting my books under his profile and I keep having to change them to appear on mine. Haha. Also, the iTunes store associates my books with his, and every now and then another website will mix up our bios and books.
For small websites, I mostly ignore it, because this other Andrew Butcher doesn't appear to be writing anymore (hasn't released anything in a while) and he writes in a different genre. I hope that once readers look a little further into the books and our profiles, they will realise we are different writers.
I do have the concern that one of my readers will buy his books thinking they are mine, but I want to keep writing under my name, so I can only try my best to separate our info.
From what I can find about this other Paige Ryan, she doesn't seem very established and hasn't released a book in about a year. I'd keep your name as it is if I were you and just try to make yourself THE Paige Ryan. Your readers will get to know you for your genre anyway. I doubt many will think those other books are yours. Also, a lot of your readers, who enjoy adult romance, probably won't jump from that to vampire/occult books (unless they already like both genres). Some would, if they really loved your writing, but most would probably wouldn't. I just don't think that, at the moment, the issue of readers confusing you with the other author will affect sales much.
It may become annoying having to keep contacting Goodreads and other websites though.
I don't like the idea of changing the spelling of your surname to something unconventional like 'Rion'.
Imagine if your books take off and someone is telling their friend about you, pronouncing 'Rion' as 'Ryan' or possibly even 'Ree-on'. Their friend will go home and search your name the way they think it would be spelt, based on how their friend said it. They'd search probably ' Paige Ryan.'
Strange spellings just equal effort for some people. I'm like, 'Who's that author I was going to search for? They had a weird name ... It was spelt differently, like the letters were mixed around or something ...' and then I give up and never search for them. Or I attempt it and spell it wrong and fail ... and give up.
I honestly don't think the legal issues of this have any stock to them. It's your birth name (I'm assuming). It's your legal name. Surely you are allowed to legally publish work under your legal name. Also, how can you know for sure that a 'Paige Rion' hasn't published something somewhere in the world?
I hope this is helpful.