How did all of Egypt hear?
Ohr ha'Chayim (to 45:1): He screamed very loudly. This shows that he was not concerned for his own shame, rather, that of his brothers. 1
Malbim: He could not refrain from crying when he told everyone to leave. "V'Lo Amad Ish" is a Ma'amar Musgar (parenthetical comment). From the crying, they understood that it was a great matter; they found out that these are his brothers only later.
Ha'amek Davar: He said, "Ani Yosef, ha'Od Avi Chai" (45:3) with emotion and crying. Those outside his house heard, and from there word went to Beis Pharaoh that Yosef found his relatives. Later, it became known that his brothers came.
Even though most Egyptians did not understand Ivri, surely word spread via those who did understand. (PF)
QUESTIONS ON RASHI
Rashi writes: "'Va'Yishma Beis Pharaoh' - I.e. Pharaoh's servants and household [heard]; it does not mean his house in the literal sense!" Why might I have thought such a thing?