"United States of America" as a Phrasal Compound

Yes, "United States of America" is a phrasal compound—a multi-word unit functioning as a single proper noun.

Breakdown:

• "United" – adjective describing the states as joined.
• "States" – noun for the constituent political units.
• "of" – preposition linking to the continent.
• "America" – noun for the continent.

Together they form the country's official name.