What exactly are the rules on non-english languages? Are pet names allowed to be written using non-english characters?
The only rule I can think of in relation to non english is this one.
However, in regards to pets, you can name them whatever you want but you can not use non-english characters. When you try to create one, the site will not allow you as the characters you can use are limited, it will appear an 'error screen' indicating the characters you're limited to use.

Non-english words are okay, though, I have some pet names in Italian c:
I have had pets for years with Hopi Latin Hindi and Greek names, but none with special characters. If you can make it work with the american alphabet I agree with Darkrai.
I've had Italian names before without problem. Except for one time where one of the mods thought I had some drug name as my UN and I was like, "Wut." That was literally it and a misread at that.

Okay. Cool. Thanks everybody. I've seen pets with names with names in other languages though?
Names in other languages are fine, the foreign letter characters and accents are not.
So I could create a Korean pet using romanized Hangul but I couldn't use that actual alphabet system to do so.

What about pets I've seen with names using foreign characters??
You can't have foreign characters, it's impossible. There is a limit in which characters you can use and if you try to write a name that contains another character it will either give an error or it will glitch.
Things like: é à ü ö ç don't work
There might be some around from before it changed though, I don't remember how it was enforced.

Wasn't enforced that strongly, unless it was made this way to avoid profanity filters
Okay, because I was looking for free names, and I stumbled across Sheep, who has 4 pets with non-english chacters as names.
Yeah, pets that were all created in 2007. That was WAY before they changed the allowable characters. But now, as everybody else has been indicating, it should not be possible.