Wikipedia is a great resource in general, but it fails in places. For example, none of the 3 sources cited for that usage of America agree with that. One points out that America (singular) can mean any of N America, S America, or the USA (but not both N and S America). The second doesn't refer to America singular at all, instead clarifying usage of "American". The third gives us some historical context - America was used to mean N + S America, but only prior to the 18th century.

I will admit that if you are from the 17th century, your confusion is reasonable, but I question how you found HN.

More importantly, at least 95% of the English-speaking world disagrees with you, and that's the real test of language and definitions.

I'm curious - in what way is Germany not an appropriate name? My understanding is that it's a translation of Deutschland, and considered an exact synonym. I'll admit that hundreds of years ago Germany or Germania meant something different from modern-day Deutschland, but I fail to see how that's relevant.