Harvard University was formerly New College until in honor of its first benefactor and English pastor John Harvard it was renamed to Harvard College in 1639.
Yes. John Harvard (1607-1638) gave half of his money and his personal library to the school when it was first built. In return, the school was named after him.
The dome is on top of a library called Rush Rhees. As far as I know, the dome does not have an official name. It's unofficial name (to many of the students) is "the Nipple of Knowledge", due to it's...