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:

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 myself use Roy/Hawkeye most of the time, 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.

These terms are of course also used in doujinshi (manga drawn by amateur artists, often based on existing works). Apart from the usual RoyAi, you can also encounter ロイ×ホークアイ (Roy x Hawkeye) and ロイ×リザ (Roy x Riza). Plenty of books centered around the Roy/Hawkeye pairing (romantically, most of the time) have been produced ever since the manga series began, and more are still produced every year.

Roy/Hawkeye is not only the most popular heterosexual Fullmetal Alchemist pairing in terms of doujinshi, but also one of the most popular guy/girl pair in the whole doujinshi-making fandom. You should be able to find books dedicated to the couple rather easily.