harry potter - Why was Snape called the Half-Blood Prince?

His mother's name was Eileen Prince, and his father was a Muggle (Tobias Snape). Thus, he gave himself the name "The Half-Blood Prince":

'I was going through the rest of the old Prophets and there was a tiny announcement about Eileen Prince marrying a man called Tobias Snape, and then later an announcement saying she'd given birth to a-'

'-murderer,' spat Harry.

'Well...yes,' said Hermione, 'So...I was sort of right. Snape must have been proud of being "half a Prince", you see? Tobias Snape was a Muggle from what it said in the Prophet.'

'Yeah, that fits,' said Harry. 'He'd play up the pure-blood side so he could get in with Lucius Malfoy and the rest of them.'

^{_{Half-Blood Prince Chapter 30: "The White Tomb"}}

It's never specified whether anyone else knew him by this name, but considering his Slytherin origin and the fact the Voldemort was on the rise, it's unlikely he was telling other student's about his half-blood status.

Well, maybe one other student...