I finally figured out how to write my name in Japanese. I've been trying to mimic the Japanese form of my name on my computer, but it never worked. I thought if I just typed normally, it would automatically convert it into Japanese. When I tried to do it, all I got was ジェッシカ, and that looked different from the original version. Now I found this
site, which tells you how to say your name in Japanese. It doesn't work in Safari though, but it should with IE.