I've also felt that, as others in this thread have mentioned, tying civs to their Earth locations is rather counterintuitive in a world which may not even have the same number of continents. I've just come up with an idea which should allow your base culture (eg European) to emerge from your location:
To begin with, civilisations have no cultures, and generic names*. At a certain point, such as Sedentary Lifestyle, you can make fairly cheap wonders for Culture: European, Culture: Asian, etc... There may be a small requirement, like needing jungle in the city vicinity for South American, but it should be probable that at least one civilisation somewhere will have that requirement. The wonders don't give any benefits in themselves, but allow you to build specific cultural wonders as usual.
However, and I'm not sure how easy this would be to code, these base culture wonders would provide that culture (probably in the form of a free Culture: [continent]) for every city within a number of tiles of it, which would preferably vary based on map size. Any city with one base culture in it could not build any (more) base culture wonders. This way, you'd end up with six overlapping geographical 'circles' for your different base cultures, and in order to get more than one (or two or three if you're very lucky with where other civs make their wonders), you'd have to expand to encompass far away cities in other 'continents'.
Oh, and names would if possible change when your civilisation acquires a culture, so they'd become the 'First European Tribe', or 'The European Water Tribe', or something like that.
*Side point here: I'd have thought it would be more thematic to come up with names which don't describe them as anything specific but are appropriate to the era, such as 'Water Tribe', or 'Red Lion Tribe'.