Let’s clear up a few issues.
The official name is: Estados Unidos de America.
It can be written with or without the article: (los) Estados Unidos de América.
If the article is included, the verb is pluralized: “Los Estados Unidos han firmado un nuevo acuerdo comercial.”
If the article is not included, the verb remains singular: “Estados Unidos firmó un nuevo acuerdo comercial.”
The abbreviation is “EE. UU.” and requires the use of the periods, as it is an abbreviation and not the initials, with a space in between as it is plural.
The initials are “EUA” which are written without any period.
The recommended adjective for denoting nationality is “estadounidense,” so as to avoid using “norteamericano” or simply “americano,” which in its strict sense refers to residents of any of the countries of the Americas.