Why would we shudder at the name Paul Revere?? He's a great patriot (and America's finest silversmith of the period) in our books.
This is like the death penalty issue in that there are degrees of degrees. The UK is a construction not all that different from the United States. The US invaded or bought territory as it expanded but then so did the Normans when they arrived in 1066. They moved in on the native Saxons and took over. They never left. Then England took Cornwall, Ireland, Wales, Man, and finally Scotland with the Act of Union. I'll give Man and the channel islands a bit of a break as they exist in a netherworld of semi-dependent states. Scotland was the closest thing to an equal joining but if you ask quite a few Scots, they'd disagree that Scotland is anything equal to England in national affairs. The only place within the isles that eventually gained freedom was Ireland and even that, from the perspective of the Irish, is only partial.
The difference in all of this is time. As the UK expanded it never released any of these countries as the US never released any of the nations within its home borders. The closest thing now is Blair's devolution scheme. The US simply had a lot more room in which to expand and did so relatively quickly and recently so it's much more present in our minds.
Another misconception is the situation with empire. At the end of WWII both the US and the UK released territories because they found that it was much cheaper and easier to pay someone to do it for them. Naturally the UK took much longer as there were so many places to withdraw from, but on the whole, the notion of empire simply changed. From political entities they evolved into economic entities. Today the UK, along with the US, back numerous regimes in former colonial areas. In some cases these are direct dictatorships or nominal democracies. Either way, they allow our economic power to be projected without the overt territorial effort. Through entities such as the IMF, World Bank, UN, "foreign aid," and secret payments, we still maintain control of many places directly or indirectly. Empire serves two needs for a nation, to secure strategic resources OR to secure strategic territory. We still hold on to Guam and Israel as the UK still holds on to Gibralter and Oman. Does the US claim Israel as territory? No. It doesn't have to. Does the UK claim Oman as territory? No. It doesn't have to. Each respective nation, however, controls the other either overtly or covertly.
The UK is ridiculously powerful in the world compared to her size. Via her intelligence, alliances, wealth, and economic apparatuses, the UK ranks as one of top five most powerful nations in the world. What used to be a territorial empire has transformed into an economic and political empire.
The other factor in all this is that UK and US view each other as necessary allies. That we share a common history, some aspects of culture, language, and strategic goals only strengthens the relationship. In WWII it quickly became obvious to both countries that each was imperative to the other's security. If the UK was taken by Hitler, then the US lost a foothold on the continent. If the US was overthrown or invaded, then the UK lost the security offered by her island status. In American military minds, the UK is the most strategic asset in all of Europe (sorry to lump you in there). Likewise, Churchill and every PM since him, has operated on the policy that the US is the final guarantor of UK sovereignty. Thatcher reiterated this, Blair acted upon it. Little remarked was that when the Falklands were invaded Reagan immediately offered to activate the US navy to assist the UK but Thatcher (wisely) declined. When the US went into Iraq, the UK followed. The two are, whether their respective peoples like it or not, joined at the hip.
English is an ethnicity in as much as the English, the Anglo-Saxons really, were, and still are, an ethnic group. Over time however, English has come to mean residents of England, not those of English ethnicity. So while there are ethnic English people, the term English now refers more to those who are born or live in England regardless of their ethnic history.
As to the business of Americans being called Americans even though the continent is shared by other nations, the same is true of the UK. Unless one identifies themselves as part of one of the subnations of the UK (English, Welsh, Scots, etc.), they're generically termed British, a reference, like American, to the geographic region even though a Welshman claiming he's British doesn't mean he's also Scots. We call ourselves American because it's the last word of our official name. United Statesians is just clumsy and besides, there are other countries, particularly Mexico, with the words, United States, in their official name. The same is true with the UK. Taken in its official long name, someone who is British would actually be claiming they're Irish! So it's much less clumsy, and perhaps more accurate, to claim to be British even if you don't necessarily live on the island of Great Britain itself.
I have always wanted to be Manx just so I can tell inquirers, in my most Austin Powersish imitation, "I'm a Man man."
For the record, I love the UK. It's a beautiful island in the parts that aren't covered in urban blight. The people are generally very friendly, particularly in Wales and Scotland, and, save for their vile native cuisine ('Ave any mutton an' eyeball pie there dearie?'} and questionable automobile electronics, I admire their achievements. There's a lot of British blood in me too and that does count for something I'm sure. I'd be proud to own a British passport even if I would be less than thrilled to be any monarch's subject.
One other thing. We talk about things that happened in history and if we speak about the sins of the fathers then we cannot visit those same sins on the sons. Both countries have had people who have done some atrocious or stupid things in the past. The nations we have now are truly built on the past, but they are not the present.