I'm a tenth generation white American. How the hell am I supposed to identify with any particular European ethnicity?
It's not my place to say how you should identify yourself, but... is 10th the furthest you go back, or the most recent? If you have 1,024 ancestors at that level, they likely weren't all born in the U.S., and some branches are more recent.
As for me, my family left a country known as Russia, from locations that are now in the countries of Belarus and Lithuania, but spoke neither Russian nor Belarussian nor Lithuanian, nor would have been considered any of those nationalities.