Guys I'm kind of hopeless after weeks of searching. My problem is the following:
When I created my Apple ID years ago I was young and didn't really understand the way Apple ID worked. I used shared it with my brother and it was perfectly fine except that he managed to mess up my iCloud mail to look like "email@example.com" instead of "firstname.lastname@example.org". Years passed and now I would really like to use the email service offered by iCloud, but seems like there is no way to change the mail address' name.
Before telling me, I know I could use an alias, but it just annoys me. I would like to have my own name on the @icloud.com mail address generated with my ID. I would simply make a fresh Apple ID, but I just managed to buy tons of apps that I'd miss. I'm open for any kind of solution. Would also transfer my purchases to the new Apple ID, but I found out that's also not possible. Merging two Apple ID's would be also nice though not possible. I'd even hack my own account if I knew and it was possible (if someone knew how, I'd give the right to).