With the abreviations for official entities, if the space allows it, I like to write what the entity is and leave the abbreviations in parenthesis (or the other way around, leave as is and explain in parenthesis - the point is: be consistent in the same document!!!). That way you avoid future confusion in case of needing the correct name for some reference.

Reg. SSA (registered in the Mexican health department)

You should not "invent" a name or try to find the equivalent in another country, because there is generally no exact equivalent.