I think humans would identify as being human rather than alien but we would still divide ourselves along arbitrary divisions like skin colour, religion or language. Much as citizens different countries identify as citizens of that nation as part of their hierarchy of self-identification, yet still further subdivide themselves in groups within the country. The discovery of aliens would merely add another level of identification.

An example of such a hierarchy as it moves from larger more general to smaller more specific (not all inclusive nor strictly linear):
Country-province-city-neighbourhood-family-individual.
Just add "Human" to the start of the list.

I think that as the former American Presidents in your post stated it would need to be an attack on all humans because they are human in order to erase all of our 'differences'.

Though how I do so wish, we could all just live as one human species.

Yes, John Lennon's "Imagine" is a great song.