the pair
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The japanese term RoyAi is widely recognized as the way to refer to the romantic relationship between Roy Mustang & Riza Hawkeye, whether it's used to refer to a fan of the relationship, a certain situation in canon that implies said pairing or a fan-related product, such as fanfiction, fanart or doujinshi.

The word is the result of combining Roy and Hawkeye's names in their katakana writings (which is used for western names, among other things). Like this:

ロイ・マスタング
ROY MUSTANG
+ リザ・ホークアイ
RIZA HAWKEYE
=
ロイアイ
ROYAI

Of course, if we were to follow the exact combination of names, the name should be RoyEye, rather than RoyAi. However, the "Ai" at the end is also understood as a play on words with the Japanese term for love, which is ai -- 愛. It's also been argued that since we're using the exact Japanese pronuntiation to spell it, it really should be RoiAi. Personally, I prefer the most common one since it sounds better, but of course you're free to use whichever you want.

Anyway, if you find the Japanese name not to your tastes, you could always use a regular way to refer to the couple. I tend to use Roy/Hawkeye rather often, since those are the names I use to talk about the characters individually. Then you've got the usual combinations: Roy/Riza or Mustang/Hawkeye. It's up to you.

It also looks like Japanese fans established a date to, er, celebrate the couple. That date is June 11th, although I've got no idea who decided it or why was that particular day chosen. If you know, I encourage you to enlighten me.