See Nick Nicholas’ answer to Who is the most famous Greek who was named Alexander in the previous 15 centuries (one for each century)? and Konstantinos Konstantinides’ answer to Who is the most famous Greek who was named Alexander in the previous 15 centuries (one for each century)?
tl;dr: for Greeks who are famous to this day, you probably have to wait until the 19th century, though Alexander (Byzantine emperor) is not nothing.