Yeah, the root words of "Europa" aren't related to that affix. Though this is as good a time as any to rage over people who confuse "utopia" with "eutopia".
On the subject of alternate naming:
Honestly, a lot of (United-States-of) Americans identify by their individual state. For that matter, identifying by state allows for easier stereotyping that doesn't confuse Texans with Kansans. I dunno if this is relevant, by brain no worky.
As I said before... it doesn't really work that well externally. There are cultural differences between the states to a certain degree, but they're largely superficial and subordinate to regional culture, which in turn is subordinate to national culture. Take, for example, my home state, Kentucky.
In varying degrees, we're known for breeding and racing thoroughbreds, for brewing bourbon (and making delicious candy with it), for being the home of an asshole who happened to steal a chicken recipe, for being on top of a bloody huge cave system, for having the best college basketball team in the country (and it sure ain't you, U of L), for our eastern part being too much like West Virginia for comfort, for being one of the two states to not really pick a side in the Civil War, for having a majority of registered Democrats but still voting in a pair of right bastards to our Senate seats, and for being the birthplace of both one of our three best presidents and a pretty cool explorer.
On the flip side, we speak the same language as the rest of the people of the U.S. with accents broadly similar to many of them, practice the same religions in the same proportions (or not) as the rest of the U.S., eat the same foods (barring a few things special to the state like our hot brown), enjoy the same entertainment, have the same political disagreements, believe in the same institutions, value the same rights and responsibilities, etc.
You could take five people, one each from Alaska, Hawaii, Maine, Florida, and Texas, put them all in a room together, and by-and-large they'd all understand and empathize with each other, share similar worldviews (regardless of their positions on them), and probably agree on two or three big things (like, "It sure is great living in America"
). Probably the points in U.S. history where you could make a valid argument for there being two distinct nations within the state would have been during the Civil War, during the height of the civil rights movement, and during the Vietnam War. Those were all times where the cultural differences went beyond the surface level and became serious rifts within society, where people disagreed (and would hate each other) over basic ideological incompatibilities.