Yes, today Tesla is a classic all-American name. I really doubt that many people heard about this obscure guy called Nikola Tesla.
Here's a census of immigrants roughly around the time Tesla was working in the U.S. (1910's), showing the relative percentages from each region (a point of comparison which is not even accounting for the ones who came from the above regions before this time): https://www2.census.gov/library/publications/decennial/1910/...
It's good to read the facts of history rather than hear trite historical narratives. In this case, it seems inbound immigrants from the Balkans made up just 1.6% in the 1910's.
I'm pretty sure the intention of saying a last name is "all-American" is to comment on the relative statistical frequency of it in a population at any given time, since that is a name people in another country (like China) would associate and know because of their likelihood of seeing it. But again, a lot of people discuss historical narratives rather than historical facts, so the above poster is not uncommon in continuing that tradition of pushing a trendy idea rather than discussing facts and information.
I don't know what narrative you're trying to debunk, because 15% year by year for years and years is high. The UK, which is a top destination for immigration, has never been close to that number until very recently. [3] But really, what I actually find weird is that you're trying to debunk some narrative.
[1] https://www2.census.gov/library/publications/decennial/1910/...
[2] https://www2.census.gov/library/working-papers/1999/demo/pop...
[2] https://en.m.wikipedia.org/wiki/Foreign-born_population_of_t....
And how do you think that ties in with the idea of a name being inherently more likely to be known by foreign groups and associated with that country?
I guess I understand your point though, that Tesla himself is very much an "American" and therefore Tesla is a household American name. Seems we've derailed very far though from the original discussion.