I think the US naming themselves after America isn't really any different from the European Union naming itself after Europe.

It's "United States OF America", not "United States that are America". It's a bunch of united states that exist in America, not the states that make up America.

Please assume that stale carrot man isn't in office and that the U.S. is currently being a reasonable and humane country that actually stands for democracy, liberty, and freedom.

It's not like the US was a leader in those things before Trump. He didn't invent the issues, he just made them more visible. The US has always overthrown democratically elected governments to install dictators, and people have complained about its own election system for ages. There's a lack of consumer and labor protections, and the fact you only have two right-wing parties and anything left of center is considered extremist opinions doesn't help at all. It's honestly hard to imagine the US actually standing for democracy, liberty, and freedom, beyond empty propaganda.