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Are all Japanese names written in Katakana? Or just foreigners?

Katakana spelling can vary, I know I changed the way I wrote my name a few times before I decided on one way that I liked. For Catherine I'd probably go with:

キャサリン

or

カスリン

depending on how you like to pronounce your name. Japanese names are written in Kanji.

That's a little confusing still, let me see if I understand...

When I looked up my name in Japanese on the baby website(cause yeah...) there wasn't anything. Kyasarin was the same. I think I was assuming that my name was an actual name in Japan, but it's not so that's why I would use Katakana. But if I was to go to Japan I would use Katakana not Kanji. Would I ever need to have my name written in Kanji?

When you name someone/something there really arn't any rules so that makes sense that Katakana would only be for names. Where as Kanji is more grammar right?

I hope that you understand what I think I understand.

Why do you drop the i?

you drop the i coz it makes it easier like ki+yo=kyo shi+yu=shu etc
And Japanese names and Chinese names both are in Kanji since kanji gives proper meaning to the names. Names in any other language are in Katakana.