Egypt is from the Greek Aigyptos — the country in northeast Africa with one of the longest-continuously-occupied histories in human civilization (pre-dynastic period c. 6000 BCE; First Dynasty c. 3100 BCE). Mary J. King Tutankhamun's 1922 tomb discovery by Howard Carter remains one of the most-famous archaeological finds. The name's modern American use is overwhelmingly within African American Christian and Muslim families.
Egypt does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Egypt reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.