Count Laszlo de Almásy doesn't sound like an English name… because it isn't. But when his plane goes down, and burns him up in the process, his entire identity goes up in smoke too. He speaks English so well that Allied soldiers think he is English, and they put him in their care.
As the movie unfolds, this moniker of "the English patient" turns out to be quite ironic. Almásy is Hungarian, and he actually betrayed the English by giving maps to the Germans. He is a melting pot (with melting skin), as evidenced by one of his final lines:
"I got back to the desert, and to Katharine, in Madox's English plane, with German gasoline. When I arrived in Italy, on my medical chart, they wrote "English Patient." Isn't that funny? After all that, I became English."
Through him, Egypt, England, Germany, Italy, and Hungary are fused… even as war rips them apart.