Cassandra Cla(i)re has written under both of those names. While she currently uses the spelling "Clare", she used Claire during her time in the Harry Potter fandom and is still known as such occasionally. There's nothing really to worry about there. In fact, her real name is Judith.
Hey! It's always good to see new people on the wiki.
There are official tutorials to help you get started on the Community Central wiki, including the Fandom University series. That's what I used to learn when I first started editing! There's also the policies page, which is specific to this wiki and tells you what is expected of editors. Thrush also wrote the discrimination policy, but considering that it's usually just me on here (and now you!), I doubt that you'll need to worry about that.
Mostly, just practice common sense. Add information you notice is missing, fix typos, remove things you think are wrong, add citations so that other editors can verify your work. If you'd like, you can also work off of my spreadsheet, which I use to keep track of what needs fixing.
As for the Discord: here's a link and welcome aboard! We're a very friendly group and we don't mind if you lurk. I'm Lee (aka enbyandroids). Can't wait to see you there!