If Americans claim to have DNA from various countries, why do they have English surnames (Smith, Johnson, Cole, Wilkins, Collins, etc)?

I understand Americans have been fully English since the 1600s, but I think they're lying about having other ancestry.

Also, where are all the Americans of Scottish, Irish, Welsh, German, Dutch, Scandinavian, Italian, Spanish, French descent? Is America an "English-only" country or something?

Does this also indicate that Americans have at least one ancestor that fought on a battlefield (musket in hand) in the Revolutionary War, and served as a sailor on a warship in the War Of 1812? And that many still have this Puritan mindset? And that England is an American's only vacation place overseas? And that American women only pursue "cute English guys"?

If Americans claim to have DNA from various countries, why do they have English surnames (Smith, Johnson, Cole, Wilkins, Collins, etc)?
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