The short answer:
You can't.
The longer answer:
Realms generally don't change their names without becoming completely different realms (eg, getting conquered, splitting in a civil war and having the newer half win, etc). However, if there is a very strong reason to change a realm's name (which is going to vary from case to case, but most commonly something like it wishes to take up the legacy of an older realm, like when Xinhai finally took all the regions belonging to the long-dead Morek and was renamd Morek Empire), you can petition the admins—that is to say, me, Vita, and Tom—and plead your case.
There is no guarantee that we will change it; indeed, statistically speaking, we're most likely to say no. But you can ask.
