What is the official name for Liore?
It's Reole.

Amestris is, canonically, an English-speaking country, and as such, all the locations are given "English" names (or, at least, names spelled out in the Latin alphabet used in English). This can be seen by looking at the original (untranslated) manga, which features a large number of character and place names written out in Latin script, rather than the katakana used for those names in dialogue. This includes the maps shown at various times in the manga.

Volume 17, page 70 offers one such example, featuring a clearly legible close-up of Liore/Reole on a map:



Additional context demonstrating that the image above is from the original Japanese language version of the manga:



Regardless of how the different parties involved may have translated it, it's quite clear that Arakawa's intended name for the city is Reole.